Question

Find the quadratic equation, whose solution set is:

(i) {3,5}

(ii) {−2, 3}

(iii) {5, −4,}

(iv) {−3, −2/5 }

Answer 1

(i) Since solution set is {3,5}

⟹ x = 3 Or x = 5

⟹ x – 3 = 0 Or x – 5 = 0

⟹ (x – 3) (x – 5) = 0

⟹ x2 – 5x – 3x + 15 = 0

⟹ x2 – 8x + 15 = 0

Which is the required equation.

(ii) Since solution set is {−2, 3}

⟹ x = – 2 Or x = 3

⟹ x + 2 = 0 Or x – 3 = 0

⟹ (x + 2) (x – 3) = 0

⟹ x2 – 3x + 2x − 6 = 0

⟹ x2 – x − 6 = 0

Which is the required equation.

(iii) Since solution set is {5,−4,}

⟹ x = 5 Or x = −4

⟹ x − 5 = 0 Or x + 4 = 0

⟹ (x − 5) (x + 4) = 0

⟹ x2 – 5x + 4x − 20 = 0

⟹ x2 – x − 20 = 0

Which is the required equation.

(iv) Since solution set is {−3, -2/5}

⟹ x = −3 Or x = −2/5

⟹ x + 3 = 0 Or 5x + 2 = 0

⟹ (x + 3) (5x + 2) = 0

⟹ 5x2 + 2x + 15x + 6 = 0

⟹ 5x2 + 17x + 6 = 0

Which is the required equation.