Relations Between Roots Solution8





The page relations between roots solution8 is containing solution of some practice questions from the worksheet relationship between roots and coefficients.

(11) If one root of the equation 2 x² - a x + 64 = 0 is twice the other, then find the value of "a"

Solution:

Roots of any quadratic equation are α and β

here one root is twice the other

α = 2 β

by comparing the given equation with general form of quadratic equation we get a = 2  b = -a and c = 64

Sum of the roots α + β = -b/a

                                = -(-a)/2

                                = a/5

Product of roots α β = c/a

                             = 64/2

                             = 32
α + β = a/5

2 β + β = a/5

 3 β = a/5

 α β = 32

 2 β (β) = 32

  2 β² = 32

  β² = 32/2

  β² = 16

   β= √16

   β= √4 x 4

   β= 4

3 β= a/5

3(4) = a/5

 12 (5) = a

  a = 60


(12) If α and β are the roots of 5 x² - p x + 1 = 0 and α - β = 1, then find p.

Solution:

Roots of any quadratic equation are α and β

by comparing the given equation with general form of quadratic equation we get a = 5  b = -p and c = 1

Sum of the roots α + β = -b/a

                                = -(-p)/5

                                = p/5

Product of roots α β = c/a

                             = 1/5

α - β = 1

 α - β = √(α + β)² - 4 α β

(p/5)² - 4 (1/5) = 1

 p²/25 - 4/5 = 1

 (p² - 20)/25 = 1

 (p² - 20) = 25

p² = 25 + 20

 p² = 45

 p = 3√5