Question

5. What are the roots of quadratic equation x2 + x-56 = 0?​

Answer 1

Answer:

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Answer 2

To find:-

$\sf{The\: roots\: of\: quadratic\: equation\: x^2+x-56}$

Solution:-

$\sf{x^2 + x - 56 = 0}$

By splitting middle term,

$\sf{\implies x^2 + 8x - 7x - 56 = 0}$

$\sf{\implies x(x+8)-7(x+8) = 0}$

$\sf{\implies (x+8)(x-7) = 0}$

Either,

$\sf{x+8 = 0}$

$\sf{\implies x = -8}$

Or,

$\sf{x-7 = 0}$

$\sf{\implies x = 7}$

$\sf{\therefore The\:zeroes\:of\:the\:quadratic\:equation\:x^2+x-56\:are\:-8\:and\:7}$

Verification:-

$\sf{Sum\:of\:zeroes = \dfrac{-Coefficient\:of\:x}{Coefficient\:of\:x^2}}$

= $\sf{-8+7 = \dfrac{-1}{1}}$

$\sf{\implies -1 = -1 \:\:\:[Verified]}$

$\sf{Product\:of\:zeroes = \dfrac{Constant\:term}{Coefficient\:of\:x^2}}$

= $\sf{-8\times7 = \dfrac{-56}{1}}$

$\sf{-56 = -56\:\:\:[Verified]}$