Question

If one zero of 2x ^2 - 3x + k is reciprocal to the other than find the value of k? Class 10th maths

Answer 1

Given: 2x²-3x+k .............eq 1
Let the 2 zeroes be α & 1/α
Quadratic form : ax²+bx+c.........eq 2
On comparing eq 1 & eq 2 we get
a=2 ,b = -3, c= k
Product of zeroes = α × 1/α = 1
Product of zeroes= c/a
1= k/ 2 
K=2

Answer 2

Final Answer :k= 2

Steps :
1) Given equation :
$2 {x}^{2} - 3x + k = 0$
2) If one zero is reciprocal of the other, then
product of the roots is 1.
=>
$\alpha \beta = 1 \\ = > \frac{k}{2} = 1 \\ = > k = 2$