Find the quadratic equation, whose solution set is:
(i) {3,5}
(ii) {−2, 3}
(iii) {5, −4,}
(iv) {−3, −2/5 }
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Find the quadratic equation, whose solution set is:
(i) {3,5}
(ii) {−2, 3}
(iii) {5, −4,}
(iv) {−3, −2/5 }
Find the quadratic equation, whose solution set is:
(i) {3,5}
(ii) {−2, 3}
(iii) {5, −4,}
(iv) {−3, −2/5 }
(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.