The page relations between roots solution1 is containing solution of some practice questions from the worksheet relationship between roots and coefficients.

(1) Find the sum and the product of the roots of the following equations.

(i) x² - 6 x + 5 = 0

**Solution:**

To find the values of a ,b and c we have to compare the given equation with the general form of quadratic equation.

a = 1 b = -6 c = 5

**Sum of roots α + β = -b/a**

**Product of roots α β = c/a**

α + β = -b/a

= -(-6)/1

= 6

Sum of roots = 6

α β = c/a

= 5/1

= 5

Product of roots = 5

(ii) k x² + r x + p k = 0

**Solution:**

To find the values of a ,b and c we have to compare the given equation with the general form of quadratic equation.

a = k b = r c = p k

**Sum of roots α + β = -b/a**

**Product of roots α β = c/a**

α + β = -b/a

= -r/k

Sum of roots = -r/k

α β = c/a

α β = p k/k

= p

Product of roots = p

(iii) 3x² - 5x = 0

**Solution:**

To find the values of a ,b and c we have to compare the given equation with the general form of quadratic equation.

a = 3 b = -5 c = 0

**Sum of roots α + β = -b/a**

**Product of roots α β = c/a**

α + β = -b/a

= -(-5)/3

= 5/3

Sum of roots = 5/3

α β = 0/3

= 0

Product of roots = 0

(iv) 8 x² - 25 = 0

**Solution:**

a = 8 b = -25 c = 0

**Sum of roots α + β = -b/a**

**Product of roots α β = c/a**

α + β = -b/a

= -(-25)/8

= 25/3

Sum of roots = 25/3

α β = c/a

α β = 0/8

= 0

Product of roots = 0

relations between roots solution1 relations between roots solution1

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