SSC CHSL 9 Jan 2017 Shift 1 Paper

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Question : 69 of 100

Marks: +1, -0

Which of the following equations has equal roots?

$x ^2 − 13x + 22 = 0$
$x^2 − 7x + 10 = 0$
$x^2 − 2x + 26 = 0$
$x^2 + 8x + 16 = 0$

Solution:

A quadratic equation :

ax^2 + bx + c = 0

has equal roots iff Discriminant,

D=b^2-4ac=0

(A) :

x ^2 − 13x + 22 = 0

⇒ D =

(−13)^2 − 4(1)(22)

= 169 − 88 = 81 ≠ 0

(B) :

x^2 − 7x + 10 = 0

⇒ D =

(−7)^2 − 4(1)(10)

= 49 − 40 = 9 ≠ 0

(C) :

x^2 − 2x + 26 = 0

⇒ D =

(−2)2 − 4(1)(26) = 4 − 104

= −100 ≠ 0

(D) :

x^2 + 8x + 16 = 0

⇒ D =

x^2 + 8x + 16 = 0

Thus, the equation :

x^2 + 8x + 16 = 0

has equal roots.

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