Find the value for p for which one root of quadratic equation px2 - 4x + 8 = 0 is 6 times the other root
Answers
Answer:
The value for p for which one root of quadratic equation px² - 4x + 8 = 0 is 6 times the other root is 3
Step-by-step explanation:
Given, equation is :
px² - 14x + 8 = 0
Let a and b be the roots of the equation
According to question,
one root of quadratic equation is 6 times the other root, that is,
b = 6a
We know for the given quadratic equation : ax² + bx + c
Sum of roots = - b / a
Product of roots = c / a
On comparing the given equation we get,
a = p , b = -14 , c = 8
Substituting values for sum and product of roots
a + b = 14 / p
ab = 8 / p
Substituting value of b as 6a in a + b
a + 6 a = 14 / p
7 a = 14 / p
a = 2 / p
Substituting value of b as 6a in a * b
a * 6 a = 8 / p
6a² = 8 / p
Dividing both sides by 2 ,
3a² = 4 / p
Substituting value of a as 2 / p
3 * ( 2 / p ) ^ 2 = 4 / p
3 * 4 / p² = 4 / p
p = 3
Hence,
The value for p for which one root of quadratic equation px² - 4x + 8 = 0 is 6 times the other root is 3