Question

find the zeroes of the quadratic polynomial x²+4x-12 and verify relationship between the zeroes and the coefficient​

Answer 1

EXPLANATION.

→ Zeroes of the quadratic polynomial

x² + 4x - 12.

→ Verify relationship between the zeroes and

coefficient.

→ Factories into middle term split.

→ x² + 4x - 12 = 0

→ x² + 6x - 2x - 12 = 0

→ x(x + 6 ) - 2 ( x + 6 ) = 0

→ ( x - 2 ) ( x + 6 ) = 0

→ x = 2 and x = -6

→ Sum = 2 + (-6) = -4.

→ Products = 2(-6) = -12.

→ Verify the relationship.

→ sum of zeroes of quadratic equation.

→ a + b = -b/a

→ a + b = -4

→ products of zeroes of quadratic equation.

→ ab = c/a

→ ab = -12

→ Hence proved.

Answer 2

Step-by-step explanation:

Given :

• the quadratic polynomial x²+4x-12

To Find :

• find the zeroes of the quadratic polynomial

• verify relationship between the zeroes and the coefficient

Solution :

$: \implies \sf \: \: \: \: \: {x}^{2} + 4x - 12 = 0\\ \\ \\ : \implies \sf \: \: \: \: \: {x}^{2} + 6x - 2x - 12 = 0 \\ \\ \\ : \implies \sf \: \: \: \: \: x(x + 6) - 2(x + 6) = 0 \\ \\ \\ : \implies \sf \: \: \: \: \: x = 2 \: and \: x = - 6$

Sum : 2 + (-6 ) = -4

product : 2 × - 6 = -12

Verification :

the product of the zeros in the given polynomial is $\sf\frac{-12}{1}= - 12$

sum of zeroes of quadratic equation.$\sf\frac{-4}{1}= - 4$

Hence proved.