Quadratic Equations – Exercise 9.7 – Class X

Find the sum and product of the roots of the quadratic equation:

1. x2 – 5x + 8 = 0
2. 3a2 – 10a – 5 = 0
3. 8m2 – m = 2
4. 6k2 – 3 = 0
5. pr2 = r – 5
6. x2 + (ab)x + (a + b) = 0

Quadratic Equation – Exercise 9.7 – Solutions:

Find the sum and product of the roots of the quadratic equation:

1. x2 – 5x + 8 = 0

Solution:

Let m and n are the roots of the quadratic equations x2 – 5x + 8 = 0 which is of the type ax2 + bx + c = 0, then, where a = 1 , b = -5 , c = 8

Formula to find the sum of the roots and product of the roots are m+n = -b/a and mn = c/a respectively.

Therefore, m + n = -b/a = -(-5)/1 = 5 and also, mn = c/a = 8/1 = 8

Thus, the sum of the roots of the quadratic  equation x2 – 5x + 8 = 0 is 5 and the product of the roots of the quadratic equation x2 – 5x + 8 = 0 is 8.

1. 3a2 – 10a – 5 = 0

Solution:

Let m and n are the roots of the quadratic equations 3a2 – 10a – 5 = 0 which is of the type ax2 + bx + c = 0, then, where a = 3 , b = -10 , c = -5

Formula to find the sum of the roots and product of the roots are m+n = -b/a and mn = c/a respectively.

Therefore, m + n = -b/a = -(-10)/3 = 10/3 and also, mn = c/a = -5/3

Thus, the sum of the roots of the quadratic  equation 3a2 – 10a – 5 = 0 is 10/3 and the product of the roots of the quadratic equation 3a2 – 10a – 5 = 0 is -5/3.

1. 8m2 – m = 2

Solution:

The given equation 8m2 – m = 2 can be written as 8m2 – m – 2 = 0

Let m and n are the roots of the quadratic equations 8m2 – m – 2 = 0 which is of the type ax2 + bx + c = 0, then, where a = 8 , b = -1 , c = -2

Formula to find the sum of the roots and product of the roots are m+n = -b/a and mn = c/a respectively.

Therefore, m + n = -b/a = -(-1)/8 = 1/8 and also, mn = c/a = -2/8 = –1/4

Thus, the sum of the roots of the quadratic  equation 8m2 – m – 2 = 0 is 1/8 and the product of the roots of the quadratic equation 8m2 – m – 2 = 0is –1/4.

1. 6k2 – 3 = 0

Solution:

The given equation 6k2 – 3 = 0 can be written as 6k2 + 0.k – 3 = 0

Let m and n are the roots of the quadratic equations 6k2 – 3 = 0 which is of the type ax2 + bx + c = 0, then, where a = 6 , b = 0 , c = -3

Formula to find the sum of the roots and product of the roots are m+n = -b/a and mn = c/a respectively.

Therefore, m + n = -b/a = -(0)/6 = 0 and also, mn = c/a = -3/6 = –1/2

Thus, the sum of the roots of the quadratic  equation 6k2 – 3 = 0 is 0 and the product of the roots of the quadratic equation 6k2 – 3 = 0 is –1/2.

1. pr2 = r – 5

Solution:

The given equation pr2 = r – 5 can be written as pr2 – r + 5 = 0

Let m and n are the roots of the quadratic equations pr2 – r + 5 = 0 which is of the type ax2 + bx + c = 0, then, where a = p , b = -1 , c = 5

Formula to find the sum of the roots and product of the roots are m+n = -b/a and mn = c/a respectively.

Therefore, m + n = -b/a = -(-1)/p = 1/p and also, mn = c/a = 5/p

Thus, the sum of the roots of the quadratic equation pr2 – r + 5 = 0 is 1/p and the product of the roots of the quadratic equation pr2 – r + 5 = 0 is 5/p.

1. x2 + (ab)x + (a + b) = 0

Solution:

Let m and n are the roots of the quadratic equations x2 + (ab)x + (a + b) = 0 which is of the type ax2 + bx + c = 0, then, where a = 1 , b = (ab) , c = (a+b)

Formula to find the sum of the roots and product of the roots are m+n = -b/a and mn = c/a respectively.

Therefore, m + n = -b/a = -ab/1 = -ab and also, mn = c/a = (a+b)/1 = (a + b)

Thus, the sum of the roots of the quadratic equation x2 + (ab)x + (a + b) = 0 is (ab) and the product of the roots of the quadratic equation x2 + (ab)x + (a + b) = 0 is (a + b).