If α and β are the roots of the equation, 2x2 –3x –6 =0, then equation whose roots are α2+2, β2 +2 is< how to solve

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Grade 12Algebra

If α and β are the roots of the equation, 2x² –3x –6 =0, then equation whose roots are α²+2, β² +2 is< how to solve

ABHAY SHANKAR

15 Years agoGrade 12

3 Answers

dvm srikant

15 Years ago

friend its we have formula

x² –x{a+b}+ab where a and b are roots of eq then find a and b from the eq and substitute in a sruare +2 and b square +2 and apply above formula (a=alpha b=beta} pls approve

mounika gajawada

15 Years ago

usin sum of roots and product of roots required eqn will be of form x²+(α²+β²+4)x + (α²+2)*(β²+2)=0

jagdish singh singh

15 Years ago

$Here $\alpha$ and $\beta$ are the roots of the equation $2x^2-3x-6=0..............(1)$\\\\ Means $x=\alpha,\beta$ be the roots of the Given Equation.\\\\ Now We have to find The equation Whose Roots are $\alpha^2+2,\beta^2+2$\\\\ Let $y=x^2+2\Leftrightarrow x=\sqrt{y-2}$\\\\ Now Put value of $x$ in equation....(1),We Get\\\\ $2(y-2)-3\sqrt{y-2}-6=0\Leftrightarrow 2y-10=3\sqrt{y-2}$\\\\ $4y^2-49y+118=0$\\\\ Means $\boxed{\boxed{4x^2-49x+118=0}}$