. If one zero of the polynomial 9x
^2 − 5x − (2k + 3) is reciprocal of the other, find the value of k.
Answers
The Given polynomial is f(x) =5x²+13x+k.
The Given polynomial is f(x) =5x²+13x+k.The quadratic equation ax² + bx + c = 0
The Given polynomial is f(x) =5x²+13x+k.The quadratic equation ax² + bx + c = 0Product of roots = c/a
The Given polynomial is f(x) =5x²+13x+k.The quadratic equation ax² + bx + c = 0Product of roots = c/aHere we have the equation 5x²+ 13x + k = 0
The Given polynomial is f(x) =5x²+13x+k.The quadratic equation ax² + bx + c = 0Product of roots = c/aHere we have the equation 5x²+ 13x + k = 0Product of roots = k/5
The Given polynomial is f(x) =5x²+13x+k.The quadratic equation ax² + bx + c = 0Product of roots = c/aHere we have the equation 5x²+ 13x + k = 0Product of roots = k/5Given that the roots are reciprocals of each other. So if one root is y, the other would be 1/y. So, their product will always be 1.
The Given polynomial is f(x) =5x²+13x+k.The quadratic equation ax² + bx + c = 0Product of roots = c/aHere we have the equation 5x²+ 13x + k = 0Product of roots = k/5Given that the roots are reciprocals of each other. So if one root is y, the other would be 1/y. So, their product will always be 1.1 = k/5
The Given polynomial is f(x) =5x²+13x+k.The quadratic equation ax² + bx + c = 0Product of roots = c/aHere we have the equation 5x²+ 13x + k = 0Product of roots = k/5Given that the roots are reciprocals of each other. So if one root is y, the other would be 1/y. So, their product will always be 1.1 = k/5k = 5.
The Given polynomial is f(x) =5x²+13x+k.The quadratic equation ax² + bx + c = 0Product of roots = c/aHere we have the equation 5x²+ 13x + k = 0Product of roots = k/5Given that the roots are reciprocals of each other. So if one root is y, the other would be 1/y. So, their product will always be 1.1 = k/5k = 5.Hence, the value of k is 5.
Answer:
Given a quadratic equation:2x² – 3x + k
Also given one of the zeros of 2x² – 3x + k is reciprocal to the other,
We need to find the value of k.
Solution
Let us assume that one zeros of the given quadratic equation be(2x² – 3x + k) be α
Hence the other zero is reciprocal of the zero. So the other zero is 1/α
As per the given equation
a = 2 b = -3 c = k
So, α x 1/α = c/a
1 = k/2
k = 2
The value of k is 2