Question

find the roots of the following quadratic equation by factorisation 2 x square minus x minus 10 is equal to zero​

Answer 1

$\mathbb{\huge{\blue{\star{SOLUTION:-}}}}$

2x²-x-10 = 0

SUM = -1

PRODUCT = -10×2 = -20

PAIR = -5,4

Hence, we get

2x² + 4x - 5x - 10 = 0

2x(x + 2)-5(x+2) = 0

(2x -5)(x + 2) = 0

______________________

This implies,

2x - 5 = 0

=> x = $\frac{5}{2}$

And,

x + 2 = 0

x = -2

_________________________

Hence, the two zeroes are:-

$\mathfrak{\huge{\orange{-2,{\frac{5}{2}}}}}$

Answer 2

$\huge\mathfrak{Answer}$

Roots of the given polynomial are -2 and 5/2

$\huge\textsf{Explanation}$

Given a polynomial p(x) = 2x² - x - 10 = 0

We have to find the roots of it by factorisation method.

What is a root of polynomial?

It is the value of x at which the value of polynomial becomes zero, that is p(x) = 0 for some value of x.

Now, let's factorise it :-

$\sf 2x^2 - x - 10 = 0 \\\\Now, split \ the \ middle \ term\\\\\implies 2x^2 - 5x + 4x - 10 = 0\\\\\implies x(2x - 5) + 2(2x - 5) = 0 \\\\\implies (x + 2)(2x - 5) = 0$

So, now, the value at which polynomial will be zero, will be

x + 2 = 0 or 2x - 5 = 0

⇒ x = -2 or x = 5/2

Hence, the roots of the given polynomial p(x) = 2x² - x - 10 = 0 are - 2 and 5/2

$\rule{200}2$