Discuss the nature of the roots of the following equations : (i) (ii) (iii) (iv) In case real roots exist , then find them.

Question

KnowledgeBoat · Accepted Answer

(i) The given equation is 3x² - 7x + 8 = 0 Comparing it with ax² + bx + c = 0 a= 3, b = -7, c = 8 Since, Discriminant 0 , hence equation has no real roots. (ii) The given equation is Comparing it with ax² + bx + c = 0 a= 1, b = , c = -4 Since, Discriminant 0 , hence equation has two distinct and real roots. By using the formula , , we obtain Hence, roots of the given equation are . (iii) The given equation is Comparing it with ax² + bx + c = 0 a= 5, b = -6 5, c = 9 Since, Discriminant = 0, hence equation has two equal and real roots. By using the formula , x = , we obtain Hence, roots of the given equation are . (iv) The given equation is . Comparing it with ax² + bx + c = 0 a= , b = -2, c = - Since, Discriminant 0 , hence equation has two distinct and real roots. By using the formula , x = , we obtain Hence, roots of the given equation are .

Mathematics

Discuss the nature of the roots of the following equations : (i) (ii) (iii) (iv) In case real roots exist , then find them.

Quadratic Equations

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Find the values of k so that the quadratic equation (4 - k)x² + 2(k + 2)x + (8k + 1) = 0 has equal roots.

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Mathematics

Discuss the nature of the roots of the following equations : (i) (ii) (iii) (iv) In case real roots exist , then find them.

Quadratic Equations

Related Questions

Solve the following equations by using formula:10ax2 - 6x + 15ax - 9 = 0 , a ≠ 0.

Solve for x using the quadratic formula. Write your answer correct to two significant figures : (x - 1)2 - 3x + 4 = 0 .

Find the values of k so that the quadratic equation (4 - k)x2 + 2(k + 2)x + (8k + 1) = 0 has equal roots.

Find the values of m so that the quadratic equation 3x2 - 5x - 2m = 0 has two distinct real roots.

Solve the following equations by using formula:
10ax² - 6x + 15ax - 9 = 0 , a ≠ 0.

Solve for x using the quadratic formula. Write your answer correct to two significant figures : (x - 1)² - 3x + 4 = 0 .

Find the values of k so that the quadratic equation (4 - k)x² + 2(k + 2)x + (8k + 1) = 0 has equal roots.

Find the values of m so that the quadratic equation 3x² - 5x - 2m = 0 has two distinct real roots.