If the quadratic expression x2-a-1x+a+14 will be a perfect square, then a=

If the quadratic expressionx2−(a−1)x+(a+14) will be perfect squarethen b2−4ac=0⇒(a−1)2−4(1)(a+14)=0⇒ a291−2a−4(4a+14)=0⇒ a2+1−2a−4a−1=0⇒ a2−6a=0⇒ a(a−6)=0⇒ a= 0, 6

If the quadratic expression x2-a-1x+a+14 will be a perfect square, then a=

If the quadratic expressionx2−(a−1)x+(a+14) will be perfect squarethen b2−4ac=0⇒(a−1)2−4(1)(a+14)=0⇒ a291−2a−4(4a+14)=0⇒ a2+1−2a−4a−1=0⇒ a2−6a=0⇒ a(a−6)=0⇒ a= 0, 6

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

If the quadratic expression $x^{2} - (a - 1) x + (a + \frac{1}{4})$ will be a perfect square, then $a =$

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

2, 6

0, 6

2, 4

0, 4

answer is D.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\begin{array}{l} I f t h e q u a d r a t i c \exp r e s s i o n \\ x^{2} - (a - 1) x + (a + \frac{1}{4}) w i l l b e p e r f e c t s q u a r e \\ t h e n b^{2} - 4 a c = 0 \\ \Rightarrow {(a - 1)}^{2} - 4 (1) (a + \frac{1}{4}) = 0 \\ \Rightarrow a^{2} 91 - 2 a - 4 (\frac{4 a + 1}{4}) = 0 \\ \Rightarrow a^{2} + 1 - 2 a - 4 a - 1 = 0 \\ \Rightarrow a^{2} - 6 a = 0 \\ \Rightarrow a (a - 6) = 0 \Rightarrow a = 0, 6 \end{array}$