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Compute the zeroes of the polynomial 4x 2 – 4x – 8. Also, establish a relationship between the zeroes and coefficients.

Compute the zeroes of the polynomial 4x2 – 4x – 8. Also, establish a relationship between the zeroes and coefficients.

 

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5964 Points
9 months ago
Dear Student

Let the given polynomial be p(x) = 4x^2– 4x – 8

To find the zeroes, take p(x) = 0

Now, factorise the equation 4x^2– 4x – 8 = 0

4x^2– 4x – 8 = 0

4(x^2– x – 2) = 0

x^2– x – 2 = 0


x^2– 2x + x – 2 = 0

x(x – 2) + 1(x – 2) = 0

(x – 2)(x + 1) = 0

x = 2, x = -1

So, the roots of 4x^2– 4x – 8 are -1 and 2.

Relation between the sum of zeroes and coefficients:

-1 + 2 = 1 = -(-4)/4 i.e. (- coefficient of x/ coefficient of x^2)

Relation between the product of zeroes and coefficients:

(-1) × 2 = -2 = -8/4 i.e (constant/coefficient of x^2)

Thanks

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