Find a quadratic polynomial whose zeros are the reciprocal of the zeros of 4 x square - 3 x minus one
Answers
Answer:
Required quadratic polynomial is x² + 3x - 4 = 0
Step-by-step explanation:
Given quadratic equation is :
4x² - 3x - 1 = 0
Solving this equation by splitting the middle term method.
4x²- 3x - 1 = 0
4x² - 4x + x - 1 = 0
4x ( x - 1 ) + 1 ( x - 1 ) = 0
( 4x + 1 ) ( x - 1 ) = 0
4x + 1 = 0 , x - 1 = 0
x= - 1 / 4 , x = 1
Therefore,
Zeroes of this quadratic equation are -1 / 4 & 1
According to the question,
Zeroes of new quadratic equation are the reciprocal of zeroes of given quadratic equation,
So the zeroes of new equation will be
a = 1 / ( - 1/4 )
a = -4
b = 1 / 1
b = 1
Sum of zeroes :
a + b = -4 + 1
a + b = -3
Product of zeroes :
ab = -4 * 1
ab = -4
We know,
The quadratic equation can be formed by :
x² - x ( a + b ) + ab = 0
Substituting the values ,
x² - x ( -3 ) + ( - 4 ) = 0
x² + 3x - 4 = 0
Hence,
Required quadratic polynomial is x² + 3x - 4 = 0
Answer:
I think it helps you....
