Question

Find the zeroes of the polynomial 2x²+5c-12

Answer 1

Given equation

$2x^{2} +5x-12=0$

Solving, we get,

$2x^{2} +5x-12=0$

$\implies 2x^{2} +8x-3x-12=0$

$\implies 2x(x+4)-3(x+4)=0$

$\implies (2x-3)(x+4)=0$

Now,

$2x-3=0$

$\implies 2x = 3$

$\implies \boxed{\boxed{\bold{ x = \dfrac{3}{2}}}}}}}}$

$x+4=0$

$\implies \boxed{\boxed{\bold{ x = -4}}}}}}}$

                                                         

Answer 2

$\huge\mathfrak{Answer:}$

Given:

• We have been given a polynomial 2x² + 5x - 12.

To Find:

• We need to find the zeroes of this polynomial.

Solution:

The Given equation is 2x² + 5x - 12.

We can find the zeroes of this polynomial by the method of splitting the middle term.

We need to find two such numbers whose sum is 5 and product is -12 × 2 = -24.

Two such numbers are 8 and -3.

Substituting the values in equation, we have

2x² + 8x - 3x - 12 = 0

=> 2x(x + 4) - 3(x + 4) = 0

=> (x + 4) (2x - 3)

Either (x + 4) = 0 or (2x - 3) = 0.

When (x + 4) = 0

=> x = -4

When (2x - 3) = 0

=> 2x = 3

=> x = 3/2

Hence, two zeroes of this polynomial are -4 and 3/2.