Question

Find the roots of equation x²-3x -10=0​

Answer 1

Answer:

x^2 - 5x +2X - 10

X(x+2)-5(X+2)

(X+2)(X-5)

roots are -2,5

Answer 2

Given:-

p(x) = x² - 3x - 10 = 0

To Find:-

roots of the equation.

Solution:-

We know to find the roots of a quadratic in the form ax² + bx + c equation, we use the formula:-

$\boxed{\bf{\underline{\dfrac{-b \pm \sqrt{b^2 -4ac}}{2a}}}}$

Here,

The given polynomial is in the form ax² + bx + c. Hence we can find the roots of this equation using the above formula.

Therefore,

p(x) = x² - 3x - 10

Here,

a = 1 (coefficient of x²), b = -3 (coefficient of x), c = -10 (constant term)

$\sf{\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}$

= $\sf{\dfrac{-(-3) \pm \sqrt{(-3)^2 - 4\times 1\times (-10)}}{2\times1}}$

= $\sf{\dfrac{3 \pm \sqrt{9 - (-40)}}{2}}$

= $\sf{\dfrac{3\pm \sqrt{9+40}}{2}}$

= $\sf{\dfrac{3\pm \sqrt{7}}{2}}$

= $\sf{\dfrac{3+7}{2} \: and\: \dfrac{3-7}{2}}$

= $\sf{\dfrac{10}{2}\:and\:\dfrac{-4}{2}}$

= $\sf{5\: and\:-2}$

Therefore the two roots of the quadratic equation x² - 3x - 10 are 5 and -2.

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Verification:-

We know,

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

And,

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

Hence, Substituting the values,

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

= $\sf{5+(-2) = \dfrac{-(-3)}{1}}$

= $\sf{3 = 3\:\:\:\:\:[Verified]}$

And,

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

= $\sf{5\times (-2) = \dfrac{-10}{1}}$

= $\sf{-10 = -10\:\:\:\:\:[Verified]}$

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