KnowledgeBoat Logo
|

Mathematics

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

  1. 74\dfrac{7}{4}

  2. 54\dfrac{5}{4}

  3. 34\dfrac{3}{4}

  4. 14\dfrac{1}{4}

Quadratic Equations

5 Likes

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 = 355\dfrac{35}{5}

⇒ 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 = 4928\dfrac{49}{28}

⇒ k = 74\dfrac{7}{4}.

Hence, option 1 is the correct option.

Answered By

1 Like

Related Questions