Find the quadratic equation whose solution set is: (i) {2, -3} (ii) {-3, 2/5} (iii) {2/5, -1/2}

(i) Since, {2, -3} is solution set. It means 2 and -3 are roots of the equation, ∴ 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. Hence, quadratic equation with solution set {2, -3} is x2 + x - 6 = 0. (ii) Since, is solution set. It means -3 and are roots of the equation, ∴ x = -3 or x = ⇒ x = -3 or 5x = 2 ⇒ x + 3 = 0 or 5x - 2 = 0 ⇒ (x + 3)(5x - 2) = 0 ⇒ (5x2 - 2x + 15x - 6) = 0 ⇒ 5x2 + 13x - 6 = 0. Hence, quadratic equation with solution set is 5x2 + 13x - 6 = 0. (iii) Since, is solution set. It means and are roots of the equation, ∴ x = or x = ⇒ 5x = 2 or 2x = -1 ⇒ 5x - 2 = 0 or 2x + 1 = 0 ⇒ (5x - 2)(2x + 1) = 0 ⇒ (10x2 + 5x - 4x - 2) = 0 ⇒ 10x2 + x - 2 = 0. Hence, quadratic equation with solution set is 10x2 + x - 2 = 0.

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Find the value of k for which x = 3 is a solution of the quadratic equation (k + 2)x² - kx + 6 = 0.
Thus, find the other root of the equation.

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Solve the following equation using quadratic formula:
x² - 4x + 1 = 0

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Mathematics

Find the quadratic equation whose solution set is: (i) {2, -3} (ii) {-3, 2/5} (iii) {2/5, -1/2}

Quadratic Equations

Related Questions

Find the value of k for which x = 3 is a solution of the quadratic equation (k + 2)x² - kx + 6 = 0.
Thus, find the other root of the equation.

Solve the following equation using quadratic formula:
x² - 4x + 1 = 0

Mathematics

Find the quadratic equation whose solution set is: (i) {2, -3} (ii) {-3, 2/5} (iii) {2/5, -1/2}

Quadratic Equations

Related Questions

Find the value of k for which x = 3 is a solution of the quadratic equation (k + 2)x2 - kx + 6 = 0.Thus, find the other root of the equation.

Solve the following equation using quadratic formula:x2 - 4x + 1 = 0

Find the value of k for which x = 3 is a solution of the quadratic equation (k + 2)x² - kx + 6 = 0.
Thus, find the other root of the equation.

Solve the following equation using quadratic formula:
x² - 4x + 1 = 0