10 grade maths> If alpha and beta are the zeros pf p(x)= ...

If alpha and beta are the zeros pf p(x)= 3x^2+5x-2 then form a quadratic polynomial whose zeros are 2alpha and 2beta

Riya , 7 Years ago

Grade 10

8 Answers

Shreya D Nanda

Last Activity: 7 Years ago

Hi Riya,

If $\alpha , and \beta$ are roots of a quadratic equation, say, $f\left ( x \right )=ax^2+ bx + c$ , then, we have

$\alpha +\beta = -b/a$ and $\alpha\beta = c/a$

So according too your question,

$p\left ( x \right ) =3x^2 +5x-2$

$\therefore \alpha +\beta =-5/3$ and $\therefore \alpha\beta =-2/3$

To form an another equation, where $2\alpha , 2\beta$ are the roots then,

$2\alpha + 2\beta= 2\left ( \alpha +\beta \right ) =2*-5/3=-10/3$ , say $-b`/a`=-10/3 \Rightarrow a`=3 , b`=10$

$[2\alpha][2\beta] =4\alpha \beta =4*-2/3= -8/3$ , say $c``/a`=-8/3 \Rightarrow a`=3 , c`=-8$

Therefore, the new quadratic polynomial, with $2\alpha , 2\beta$ as roots, is

$p`\left ( x \right ) =a`x^2+b`x +c`$

$\Rightarrow p`\left ( x \right ) =3x^2+10x -8`$ .

hope it is clear,,

sachin

Last Activity: 7 Years ago

If $\alpha , and \beta$ are roots of a quadratic equation, say, $f\left ( x \right )=ax^2+ bx + c$ , then, we have

$\alpha +\beta = -b/a$ and $\alpha\beta = c/a$

So according too your question,

$p\left ( x \right ) =3x^2 +5x-2$

$\therefore \alpha +\beta =-5/3$ and $\therefore \alpha\beta =-2/3$

To form an another equation, where $2\alpha , 2\beta$ are the roots then,

$2\alpha + 2\beta= 2\left ( \alpha +\beta \right ) =2*-5/3=-10/3$ , say $-b`/a`=-10/3 \Rightarrow a`=3 , b`=10$

$[2\alpha][2\beta] =4\alpha \beta =4*-2/3= -8/3$ , say $c``/a`=-8/3 \Rightarrow a`=3 , c`=-8$

Therefore, the new quadratic polynomial, with $2\alpha , 2\beta$ as roots, is

$p`\left ( x \right ) =a`x^2+b`x +c`$

$\Rightarrow p`\left ( x \right ) =3x^2+10x -8`$ .

sachin

Last Activity: 7 Years ago

If $\alpha , and \beta$ are roots of a quadratic equation, say, $f\left ( x \right )=ax^2+ bx + c$ , then, we have

$\alpha +\beta = -b/a$ and $\alpha\beta = c/a$

So according too your question,

$p\left ( x \right ) =3x^2 +5x-2$

$\therefore \alpha +\beta =-5/3$ and $\therefore \alpha\beta =-2/3$

To form an another equation, where $2\alpha , 2\beta$ are the roots then,

$2\alpha + 2\beta= 2\left ( \alpha +\beta \right ) =2*-5/3=-10/3$ , say $-b`/a`=-10/3 \Rightarrow a`=3 , b`=10$

$[2\alpha][2\beta] =4\alpha \beta =4*-2/3= -8/3$ , say $c``/a`=-8/3 \Rightarrow a`=3 , c`=-8$

Therefore, the new quadratic polynomial, with $2\alpha , 2\beta$ as roots, is

$p`\left ( x \right ) =a`x^2+b`x +c`$ .

$\Rightarrow p`\left ( x \right ) =3x^2+10x -8`$ .

sachin

Last Activity: 7 Years ago

If $\alpha , and \beta$ are roots of a quadratic equation, say, $f\left ( x \right )=ax^2+ bx + c$ , then, we have

$\alpha +\beta = -b/a$ and $\alpha\beta = c/a$

So according too your question,

$p\left ( x \right ) =3x^2 +5x-2$

$\therefore \alpha +\beta =-5/3$ and $\therefore \alpha\beta =-2/3$

To form an another equation, where $2\alpha , 2\beta$ are the roots then,

$2\alpha + 2\beta= 2\left ( \alpha +\beta \right ) =2*-5/3=-10/3$ , say $-b`/a`=-10/3 \Rightarrow a`=3 , b`=10$

$[2\alpha][2\beta] =4\alpha \beta =4*-2/3= -8/3$ , say $c``/a`=-8/3 \Rightarrow a`=3 , c`=-8$

Therefore, the new quadratic polynomial, with $2\alpha , 2\beta$ as roots, is

$p`\left ( x \right ) =a`x^2+b`x +c`$

$\Rightarrow p`\left ( x \right ) =3x^2+10x -8`$ …,.,.

sachin

Last Activity: 7 Years ago

If $\alpha , and \beta$ are roots of a quadratic equation, say, $f\left ( x \right )=ax^2+ bx + c$ , then, we have

$\alpha +\beta = -b/a$ and $\alpha\beta = c/a$

So according too your question,

$p\left ( x \right ) =3x^2 +5x-2$

$\therefore \alpha +\beta =-5/3$ and $\therefore \alpha\beta =-2/3$

To form an another equation, where $2\alpha , 2\beta$ are the roots then,

$2\alpha + 2\beta= 2\left ( \alpha +\beta \right ) =2*-5/3=-10/3$ , say $-b`/a`=-10/3 \Rightarrow a`=3 , b`=10$

$[2\alpha][2\beta] =4\alpha \beta =4*-2/3= -8/3$ , say $c``/a`=-8/3 \Rightarrow a`=3 , c`=-8$

Therefore, the new quadratic polynomial, with $2\alpha , 2\beta$ as roots, is

$p`\left ( x \right ) =a`x^2+b`x +c`$

$\Rightarrow p`\left ( x \right ) =3x^2+10x -8`$ .//,/,/,/

sachin

Last Activity: 7 Years ago

If $\alpha , and \beta$ are roots of a quadratic equation, say, $f\left ( x \right )=ax^2+ bx + c$ , then, we have

$\alpha +\beta = -b/a$ and $\alpha\beta = c/a$

So according too your question,

$p\left ( x \right ) =3x^2 +5x-2$

$\therefore \alpha +\beta =-5/3$ and $\therefore \alpha\beta =-2/3$

To form an another equation, where $2\alpha , 2\beta$ are the roots then,

$2\alpha + 2\beta= 2\left ( \alpha +\beta \right ) =2*-5/3=-10/3$ , say $-b`/a`=-10/3 \Rightarrow a`=3 , b`=10$

$[2\alpha][2\beta] =4\alpha \beta =4*-2/3= -8/3$ , say $c``/a`=-8/3 \Rightarrow a`=3 , c`=-8$

Therefore, the new quadratic polynomial, with $2\alpha , 2\beta$ as roots, is

$p`\left ( x \right ) =a`x^2+b`x +c`$

$\Rightarrow p`\left ( x \right ) =3x^2+10x -8`$ .././/././.....

soumya ranjan prusty

Last Activity: 7 Years ago

If $\alpha , and \beta$ are roots of a quadratic equation, say, $f\left ( x \right )=ax^2+ bx + c$ , then, we have

$\alpha +\beta = -b/a$ and $\alpha\beta = c/a$

So according too your question,

$p\left ( x \right ) =3x^2 +5x-2$

$\therefore \alpha +\beta =-5/3$ and $\therefore \alpha\beta =-2/3$

To form an another equation, where $2\alpha , 2\beta$ are the roots then,

$2\alpha + 2\beta= 2\left ( \alpha +\beta \right ) =2*-5/3=-10/3$ , say $-b`/a`=-10/3 \Rightarrow a`=3 , b`=10$

$[2\alpha][2\beta] =4\alpha \beta =4*-2/3= -8/3$ , say $c``/a`=-8/3 \Rightarrow a`=3 , c`=-8$

Therefore, the new quadratic polynomial, with $2\alpha , 2\beta$ as roots, is

$p`\left ( x \right ) =a`x^2+b`x +c`$ .

$\Rightarrow p`\left ( x \right ) =3x^2+10x -8`$ .

soumya ranjan prusty

Last Activity: 7 Years ago

If $\alpha , and \beta$ are roots of a quadratic equation, say, $f\left ( x \right )=ax^2+ bx + c$ , then, we have

$\alpha +\beta = -b/a$ and $\alpha\beta = c/a$

So according too your question,

$p\left ( x \right ) =3x^2 +5x-2$

$\therefore \alpha +\beta =-5/3$ and $\therefore \alpha\beta =-2/3$

To form an another equation, where $2\alpha , 2\beta$ are the roots then,

$2\alpha + 2\beta= 2\left ( \alpha +\beta \right ) =2*-5/3=-10/3$ , say $-b`/a`=-10/3 \Rightarrow a`=3 , b`=10$

$[2\alpha][2\beta] =4\alpha \beta =4*-2/3= -8/3$ , say $c``/a`=-8/3 \Rightarrow a`=3 , c`=-8$

Therefore, the new quadratic polynomial, with $2\alpha , 2\beta$ as roots, is

$p`\left ( x \right ) =a`x^2+b`x +c`$ .

$\Rightarrow p`\left ( x \right ) =3x^2+10x -8`$ . ok....................................

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10 grade maths> If alpha and beta are the zeros pf p(x)= ...

If alpha and beta are the zeros pf p(x)= 3x^2+5x-2 then form a quadratic polynomial whose zeros are 2alpha and 2beta

Riya , 7 Years ago

Shreya D Nanda

sachin

sachin

sachin

sachin

sachin

soumya ranjan prusty

soumya ranjan prusty

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