Question

Find the zeroes of the quadratic equation x²–7x+12 and verify the relationship
between the zeroes and the coefficients of the polynomial​

Answer 1

Answer:

p(x)=x^2-7x+12

by mid term splitting

x^2-3x-4x+12

x(x-3)-4(x-3)

(x-4),(x-3)

zeros=4,3

relation b/w coefficients and polynomial:-

sum of zeros=α+β

-b/a=α+β

-(-7)/1=4+3

7=7

product of zeros=αβ

c/a=αβ

12/1=4*3

12=12

Answer 2

Step-by-step explanation:

Given:-

The Quadratic Polynomial x²–7x+12

To find:-

Find the zeroes of the quadratic polynomial x²–7x+12 and verify the relationship between the zeroes and the coefficients of the polynomial ?

Solution:-

Given quadratic polynomial is X^2-7X +12

=>X^2-3X-4X+12

=>X(X-3) -4(X-3)

=>(X-3)(X-4)

To get zeroes of quadratic polynomial we equate with zero

=>(X-3)(X-4) = 0

=>X-3 = 0 or (X-4) = 0

=>X = 3 and X = 4

The zeroes are 3 and 4

Relationship between the zeroes and the coefficients:-

On Comparing X^2-7X+12 with the standard quadratic Polynomial aX^2+bX+C

a = 1

b= -7

c = 12

and the zeores are 3 and 4

Let α = 3 and β = 4

I) Sum of the zeroes = α+β = 3+4 = 7

Now -Coefficient of X/ Coefficient of X^2

=>-b/a

=>-(-7)/1

=>7

α+β = -b/a

ii) Product of the zeroes = αβ=3×4 = 12

=>Constant term /Coefficient of X^2

=>c/a

=>12/1

=>12

αβ = c/a

Verified the relationship between the zeroes and the coefficients of the given Polynomial.

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