Question

find the zeroes of the quadratic polynomial given below. find the sum and products of the zeroes and verify relationship of terms in the polynomial.
2. P of x = x square _4x+3​

Answer 1

Given:

• P(x) = x² - 4x +3

To find :

• The zeroes of the quadratic polynomial .

• To verify the relationship .

Solution :

•x² - 4x + 3 = 0

Split the middle term :

=> x² - 3x - x + 3 = 0

=> x ( x - 3) - 1 ( x - 3 ) = 0

=> (x - 1)( x - 3 ) = 0

• x - 1 = 0

=> x = 1 .

• x - 3 = 0

=> x = 3 .

Hence , the zeroes are 1 and 3 .

Now , verification :

• x² - 4x +3 .

compare with ax² + bx + c we get ,

• a = 1 , b = -4 and c = 3 .

As we know that :

• Sum of Zeroes = -b/a

=> 1 + 3 = -(-4)/1

=> 4 = 4

LHS = RHS .

NOW ,

• Product of Zeroes = c/a

=> 1(3)= 3/1

=> 3 = 3

LHS = RHS .

Hence, Verified .

Answer 2

x²-4x+3

=( x-1 )( x- 3)

= x = 1 and 3

sum = -b/a

= 1 +3 = --4/1

=4= 4 verified .

product = c/a

= 1 ×3 = 3/1

= 3 = 3