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

- Back to worksheet
- Practice problems on nature of roots
- Practical problems in quadratic equation
- Framing quadratic equation from roots
- Square root
- Solving linear equation in cross multiple method
- Solving linear equations in elimination method