Question

Q.7. Find the sum and product of zeroes of the quadratic polynomial 2x2-7x+5 and verify the
results.
(3 marks)​

Answer 1

Solution :

• 2x²-7x +5 =0

=> 2x²-5x-2x+5 = 0

=> x ( 2x-5)-1(2x-5)=0

=> (x-1)(2x-5) = 0

• x-1=0

=> x= 1

• 2x-5=0

=> x = 5/2.

Now , Verification :

Here , a= 2 ,b= -7 and c = 5

As we know that :

• Sum of zeroes = -b/a

• 5/2+1 = -(-7)/2

• 7/2 = 7/2

LHS = RHS.

• Product of zeroes = c/a

=> 1(5/2)= 5/2

=> 5/2 = 5/2.

LHS = RHS ..

Hence, verified .

Answer 2

2x²-7x+5 = 0

=) 2x²-(5+2)x+5 = 0

=) 2x²-5x-2x+5 = 0

=) x(2x-5)-1(2x-5) = 0

=) (2x-5)(x-1) = 0

x = 5/2 ; x = 1

Verifying

(i) 2x²-7x+5 = 0

=) (2×25/4)-(7×5/2)+5 = 0

=) 50/4 - 35/2 + 5 = 0

=) (50-70+20)/2 = 0

=) (50-50)/2 = 0

=) 0/2 = 0

=) 0 = 0 [LHS = RHS]

(ii) 2x²-7x+5 = 0

=) (2×1)-(7×1)+5 = 0

=) 2-7+5 = 0

=) 2-2 = 0 [LHS = RHS]