Find the discriminant of the following quadratic equations and hence find the nature of roots :
(i) 3x² - 5x - 2 = 0
(ii) 2x² - 3x + 5 = 0
(iii) 16x² - 40x + 25 = 0
(iv) 2x² + 15x + 30 = 0

Question

Find the discriminant of the following quadratic equations and hence find the nature of roots : (i) 3x² - 5x - 2 = 0 (ii) 2x² - 3x + 5 = 0 (iii) 16x² - 40x + 25 = 0 (iv) 2x² + 15x + 30 = 0

KnowledgeBoat · Accepted Answer

(i) The given equation is 3x² - 5x - 2 = 0. Comparing it with ax² + bx + c = 0, we get a = 3 , b = -5 , c = -2 ∴ Discriminant = b² - 4ac Putting values of a, b, c in formula Discriminant = 49; Hence, the given equation has two distinct real roots. (ii) The given equation is 2x² - 3x + 5 = 0. Comparing it with ax² + bx + c = 0, we get a = 2 , b = -3 , c = 5 ∴ Discriminant = b² - 4ac Putting values of a, b, c in formula Discriminant = -31; Hence, the given equation has no real roots. (iii) The given equation is 16x² - 40x + 25 = 0. Comparing it with ax² + bx + c = 0, we get a = 16 , b = -40 , c = 25 ∴ Discriminant = b² - 4ac Putting values of a, b, c in formula Discriminant = 0; Hence, the given equation has two equal real roots. (iv) The given equation is 2x² + 15x + 30 = 0. Comparing it with ax² + bx + c = 0, we get a = 2 , b = 15 , c = 30 ∴ Discriminant = b² - 4ac Putting values of a, b, c in formula Discriminant = -15; Hence, the given equation has no real roots.

Mathematics

Find the discriminant of the following quadratic equations and hence find the nature of roots :
(i) 3x² - 5x - 2 = 0
(ii) 2x² - 3x + 5 = 0
(iii) 16x² - 40x + 25 = 0
(iv) 2x² + 15x + 30 = 0

Quadratic Equations

Related Questions

Solve the equation 5x² - 3x - 4 = 0 and give your answer correct to 3 significant figures.

Mathematics

Find the discriminant of the following quadratic equations and hence find the nature of roots :(i) 3x2 - 5x - 2 = 0(ii) 2x2 - 3x + 5 = 0(iii) 16x2 - 40x + 25 = 0(iv) 2x2 + 15x + 30 = 0

Quadratic Equations

Related Questions

Solve the equation 5x2 - 3x - 4 = 0 and give your answer correct to 3 significant figures.

Find the discriminant of the following quadratic equations and hence find the nature of roots :
(i) 3x² - 5x - 2 = 0
(ii) 2x² - 3x + 5 = 0
(iii) 16x² - 40x + 25 = 0
(iv) 2x² + 15x + 30 = 0

Solve the equation 5x² - 3x - 4 = 0 and give your answer correct to 3 significant figures.