Question

38. Find the zeroes of the quadratic polynomial

X^2- 7x + 12 and verify the relational

between the zeroes and the coefficients of the polynomial​

Answer 1

Answer:

X = 3

or

X =4

X^2-4x-3x+12

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

(x-3)(x-4)

x=3

or

x=4

Answer 2

Step-by-step explanation:

Given:-

The quadratic polynomial X^2- 7x + 12

To find:-

Find the zeroes of the quadratic polynomial and

verify the relationship between the zeroes and the coefficients of the polynomial.

Solution:-

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

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

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

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

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

To get zeroes we equate the P(x) to zero.

=>P(X)=0

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

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

=>X=3 or X= 4

The zeroes of the quadratic polynomial are 3 and 4

Let

α= 3

β = 4

On comparing the given pilynomial with ax^2+bx+c we get

a= 1

b=-7

c=12

Relationship between the coefficients and the zeores:-

1)Sum of the zeroes :-

α + β = 3+4 = 7

-b/a = -(-7)/1=7

α + β = -b/a

2) Product of the zeroes:-

α β = 3×4 = 12

c/a = 12/1=12

αβ = c/a

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

Used formulae:-

• Sum of the zeroes = -b/a
• Product of the zeroes = c/a