Question

If the sum of the zeros of the quadratic polynomial $f(x)= kx^{2}-3x+5$ is 1,write the value of k.

Answer 1

SOLUTION :

Let α  and β are the zeroes of the quadratic polynomial

Given : the quadratic polynomial : kx² - 3x + 5 and α + β = 1

On comparing with ax² + bx + c,

a = k , b= - 3 , c= 5

Sum of the zeroes = −coefficient of x / coefficient of x²

α + β  = -b/a  

1 = -(-3)/k

1 = 3/k

k × 1 = 3  

k = 3

Hence, the value of k is 3 .

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Answer 2

Solution :

Compare f(x) = kx²-3x+5 with

ax² + bx + c = 0. we get

a = k , b = -3 , c = 5

Sum of the zeroes = 1 [ given ]

=> ( -b/a ) = 1

=> -(-3)/k = 1

=> 3/k = 1

=> 3 = k

Therefore ,

k = 3

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