Discuss the nature of the roots of the following quadratic equations : (i) (ii) (iii) (iv)

Question

KnowledgeBoat · Accepted Answer

(i) The given equation is . Comparing it with ax² + bx + c = 0, we get a = 3 , b = , c = 4 ∴ Discriminant = b² - 4ac Putting values of a, b, c in formula Hence the given equation has two equal real roots. (ii) The given equation is . Comparing it with ax² + bx + c = 0, we get a = 1 , b = , c = 4 ∴ Discriminant = b² - 4ac Putting values of a, b, c in formula Hence the given equation has no real roots. (iii)The given equation is -2x² + x + 1 = 0. Comparing it with ax² + bx + c = 0, we get a = -2 , b = 1 , c = 1 ∴ Discriminant = b² - 4ac Putting values of a, b, c in formula Hence, the given equation has two distinct real roots. (iv) The given equation is . Comparing it with ax² + bx + c = 0, we get a = , b = -5 , c = ∴ Discriminant = b² - 4ac Putting values of a, b, c in formula Hence, the given equation has two distinct real roots.

Mathematics

Discuss the nature of the roots of the following quadratic equations : (i) (ii) (iii) (iv)

Quadratic Equations

Related Questions

Solve the following quadratic equation for x and give your answer correct to three significant figures :
2x² - 10x + 5 = 0

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

Without solving the following quadratic equations, find the value of 'p' for which the given equations have real and equal roots :
(i) px² - 4x + 3 = 0
(ii) x² + (p - 3)x + p = 0

Mathematics

Discuss the nature of the roots of the following quadratic equations : (i) (ii) (iii) (iv)

Quadratic Equations

Related Questions

Solve the following quadratic equation for x and give your answer correct to three significant figures :2x2 - 10x + 5 = 0

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

Without solving the following quadratic equations, find the value of 'p' for which the given equations have real and equal roots :(i) px2 - 4x + 3 = 0(ii) x2 + (p - 3)x + p = 0

Solve the following quadratic equation for x and give your answer correct to three significant figures :
2x² - 10x + 5 = 0

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

Without solving the following quadratic equations, find the value of 'p' for which the given equations have real and equal roots :
(i) px² - 4x + 3 = 0
(ii) x² + (p - 3)x + p = 0