Question

find the zeros of quardretic polynomial x²+7x+12 and verify the relation between zeros and it's codfeciant​

Answer 1

Step-by-step explanation:

Given:-

Quadratic polynomial is x^2+7x+12

To find:-

1)Find the zeros of quardratic polynomial x^2+7x+12

2) Verify the relation between zeros and it's coefficients?

Solution:-

Given quadratic polynomial is x^2+7x+12

Finding the zeroes :-

Let P(x) = x^2+7x+12

To get the zeores of P(x) we write P(x) = 0

=> x^2+7x+12=0

=> x^2+3x+4x+12 = 0

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

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

=> x+3 = 0 or x+4 = 0

=> x = -3 and x = -4

Zeroes are -3 and -4

Relationship between the zeroes and the coefficients:-

P(x) = x^2+7x+12

On Comparing this with the standard quadratic Polynomial ax^2+bx+c

a = 1

b = 7

c = 12

We have zeroes = -3 and -4

Let α = -3 and β = -4

Sum of the zeroes

= α + β

= (-3) + (-4)

= -3-4

= -7

= -(7)/1

= - Coefficient of x/ Coefficient of x^2

= - b/a

Product of the zeroes

= αβ

= (-3) × (-4)

= 12

= 12/1

= Constant term/ Coefficient of x^2

= c/a

Verified the relationship between the zeroes and the coefficients.

Answer:-

i) Zeroes are -3 and -4

ii)Verified the relationship between the zeroes and the coefficients.

Used formulae:-

• The standard quadratic Polynomial ax^2+bx+c
• Sum of the zeroes= α + β = -b/a
• Product of the zeroes= αβ=c/a