Question

find the zeros of the polynomial 2 X^2 + 3 x - 6​

Answer 1

Given:

A polynomial 2x²+3x-6

To Find:

• Zeroes of the given polynomial

Solution:

Let given polynomial be p(x)= 2x²+3x-6

Since, it is a quadratic polynomial so it will have two zeroes

Now, let 'a' be one of the zero of given polynomial, then it will satisfy the given polynomial

i.e. p(a)= 0

Now,

p(a)= 2a²+3a-6= 0

So, by using quadratic formula, we will determine the zeroes of the above equation

We know that, according to quadratic formula , roots of the equation of the form of ax²+bx+c= 0 are

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

So, roots of the equation 2a²+3a-6= 0 are

$\sf{a=\dfrac{-3\pm\sqrt{(3)^{2}-4(2)(-6)}}{2(2)}}$

$\sf{a=\dfrac{-3\pm\sqrt{9+48}}{4}}$

$\sf{a=\dfrac{-3\pm\sqrt{57}}{4}}$

$\sf{a=\dfrac{-3+\sqrt{57}}{4},\dfrac{-3-\sqrt{57}}{4}}$

Hence, roots of the given polynomial are $\sf\green{\dfrac{-3+\sqrt{57}}{4}}$ and $\sf\orange{\dfrac{-3-\sqrt{57}}{4}}$.