The coefficient of x in the quadratic equation x2-p x-q-0 was taken as -14 in place of -10- its roots were found to be 6-4 - If - - are the roots of correct equation- then the value of -2-2 must be equal to-

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Standard X

Mathematics

Sum and Product of Roots of a Quadratic Equation

The coefficie...

Question

The coefficient of x in the quadratic equation $x^{2} + p x + q = 0$ was taken as -14 in place of -10, its roots were found to be 6, 4. If α, β are the roots of correct equation, then the value of $α^{2} + β^{2}$ must be equal to

__

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Solution

q = 24 [product of roots = 6 $\times$ 4]

p = -10(negative of Sum of the roots)

$∴$ The equation is $x^{2} - 10 x + 24 = 0$

The roots are 6, 4

$∴ α^{2} + β^{2} = 6^{2} + 4^{2}$

= 36 + 16

= 52

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The coefficient of x in the quadratic equation x2+px+q=0 was taken as -14 in place of -10, its roots were found to be 6, 4. If α, β are the roots of correct equation, then the value of α2+β2 must be equal to __

q = 24 [product of roots = 6 × 4] p = -10(negative of Sum of the roots) ∴ The equation is x2−10x+24=0 The roots are 6, 4 ∴ α2+β2=62+42 = 36 + 16 = 52

The coefficient of x in the quadratic equation $x^{2} + p x + q = 0$ was taken as -14 in place of -10, its roots were found to be 6, 4. If α, β are the roots of correct equation, then the value of $α^{2} + β^{2}$ must be equal to

__

q = 24 [product of roots = 6 $\times$ 4]

p = -10(negative of Sum of the roots)

$∴$ The equation is $x^{2} - 10 x + 24 = 0$

The roots are 6, 4

$∴ α^{2} + β^{2} = 6^{2} + 4^{2}$

= 36 + 16

= 52