If -5 is a root of the quadratic equation 2x^2 + px - 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, then the value of k is: 1. 7/4 2. 5/4 3. 3/4 4. 1/4

Question

KnowledgeBoat · Accepted Answer

Given, -5 is a root of the quadratic equation 2x2 + px - 15 = 0. Substituting value of x = -5 in 2x2 + px - 15 = 0, we get: ⇒ 2(-5)2 + p(-5) - 15 = 0 ⇒ 2 × 25 - 5p - 15 = 0 ⇒ 50 - 5p - 15 = 0 ⇒ 35 - 5p = 0 ⇒ 5p = 35 ⇒ p = ⇒ p = 7. Substituting value of p in p(x2 + x) + k = 0, we get: ⇒ 7(x2 + x) + k = 0 ⇒ 7x2 + 7x + k = 0 Comparing 7x2 + 7x + k = 0 with ax2 + bx + c = 0 we get, a = 7, b = 7 and c = k. Since equation has equal roots, ⇒ Discriminant = 0 ⇒ b2 - 4ac = 0 ⇒ (7)2 - 4(7)(k) = 0 ⇒ 49 - 28k = 0 ⇒ 28k = 49 ⇒ k = ⇒ k = . Hence, option 1 is the correct option.

Mathematics

If -5 is a root of the quadratic equation 2x^2 + px - 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, then the value of k is: 1. 7/4 2. 5/4 3. 3/4 4. 1/4

Quadratic Equations

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Mathematics

If -5 is a root of the quadratic equation 2x^2 + px - 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, then the value of k is: 1. 7/4 2. 5/4 3. 3/4 4. 1/4

Quadratic Equations

Related Questions

What is the nature of the roots of the equation, 2x2 - 6x + 3 = 0?rational and unequalirrational and unequalreal and equalimaginary and unequal

What is the nature of the roots of the equation, 2x² - 6x + 3 = 0?
rational and unequal
irrational and unequal
real and equal
imaginary and unequal