Question

find the zeros of the quadratic polynomial 8Xsq+2x-15 and verify the relationship between the zeroes and it's coefficients​

Answer 1

Answer:

Step-by-step explanation:

a is co efficient of x sq term

b is co efficient of x term

c is constant

8x^2+2x-15

8x^2-10x+12x-15

2x(4x-5)+3(4x-5)

(2x+3)(4x-5)

zeroes are -3/2 and +5/4

sum of zeroes=-3/2+5/4=-6+5/4=-1/4=-b/a

product of zeroes=-3/2*5/4=-15/8=c/a

Answer 2

$\rule{300}2$

Your Answer:

How to find zeroes of Quadratic Equation.

• Factorization Method
• Quadratic Formula
• Completing Square Method.

Here I am gonna use Factorization Method.

8x²+2x-15

Finding zeroes

8x² + (12-10)x -15

= 8x² +12x -10x -15

= 4x(2x+3) -5(2x+3)

= (4x-5) ( 2x+3)

(4x-5)(2x+3) are the two factors.

To find the zeroes we have to equate them with zero.

Equating (4x-5) with zero

4x-5=0

4x=5

x=5/4

Equating (2x+3) with zero

2x+3=0

2x= -3

x= -3/2

So the zeroes are 5/4 and -3/2

Verifying the relationship.

α+β= -b/a and αβ= c/a where α and β are the zeroes.

So, α+β= 5/4 -3/2 = -1/4

and αβ= (5/4)(-3/2) = -15/8

And -b/a = -(2/8) = -1/4

c/a = -15/8

So, α+β= -b/a verified

and αβ = c/a verified.

$\rule{300}2$