Question

2x²+5x-12 find the Zeros of the following quadratic polynomial and verify the relationship between the zeros and the coefficients

Answer 1

Given, polynomial is 2x² + 5x - 12.

We have to find the zeros of the quadratic polynomial and verify the relationship between the zeros and the coefficients.

Now,

The above quadratic equation is in the form ax² + bx + c = 0.

Where, a = 2, b = 5 and c = -12

By Splitting the middle term

→ 2x² + 5x - 12 = 0

→ 2x² + 8x - 3x - 12 = 0

→ 2x(x + 4) -3(x + 4) = 0

→ (x + 4)(2x - 3) = 0

On comparing we get,

→ x = -4, 3/2

Therefore, zeros of the quadratic polynomial 2x² + 5x - 12 are -4 and 3/2.

Verification

Sum of zeros = -b/a

-4 + 3/2 = -5/2

(-8 + 3)/2 = -5/2

-5/2 = -5/2

Product of zeros = c/a

(-4) × (3/2) = -12/2

(-2) × 3 = -6

-6 = -6

Answer 2

Given polynomial:-

$\bold{2x^2+5x-12}$

To find:-

• The zeros of the given polynomial.

• verify the relationship between the zeros and the coefficients.

Solution:-

$2x^2+5x-12\\2x^2-3x+8x-12=0\\\x(2x-3)+4(2x-3)=0\\(2x-3)(x+4)=0\\2x-3=0\ or\ x+4=0$

$\boxed{x=\frac{3}{2}}\ or\ \boxed{x=-4 }$

In the given polynomial, a = 2, b = 5 & c = -12.

Let α be 3/2 and β be -4.

• α + β = -b/a

• ⇒α + β = -5/2

• 3/2 + (-4) = (3-8)/2

• 3/2 + (-4) = -5/2

Hence, the relation is verified here (sum of the zeroes).

• αβ = c/a

• ⇒αβ = -12/2

• ⇒αβ = -6

• 3/2*-4 = (3*-4)/2

• ⇒3/2*-4 = -12/2

• ⇒3/2*-4 = -6

Hence, the relation is verified here (product of the zeroes).

∴The relationship between the zeros and the coefficients is verified.