NTSE Stage 2 SAT 2017 Question Paper

Question : 48 of 100

Marks: +1, -0

If the quadratic equation

\x^2+ \bx + 72 = 0

has two distinct integer roots, then the number of all possible value for b is-

Solution:

Reason :
For quadratic equation :

\x^2+ \bx + 72=0

\α+\β=72

[using product of roots]
Now, for

\α×\β=72,

possible positive values are

\α= 1 \;&\; \β= 72 ⇒\b = – 73

\α = 2 \;&\;\β= 36 ⇒\b = – 38

\α= 3 \;&\;\β= 24 ⇒\b = – 27

\α = 4 \;&\;\β= 18 ⇒\b = – 22

\α = 6 \;&\;\β= 12 ⇒\b = – 18

\α= 8 \;&\;\β= 9 ⇒ \b = – 17

{using sum of roots)
Nor for αβ= 72, possible negative values are

\α= –1 \;&\;\β= –72 ⇒\b= 73

\α= –2 \;&\;\β= –36⇒\b= 38

\α= –3 \;&\;\β = –24 ⇒\b= 27

\α= –4 \;&\;\β= –18 ⇒\b = 22

\α= –6 \;&\;\β= –12 ⇒\b= 18

\α= –8 \;&\;\β= –9 ⇒\b = 17

hence total number of possible value of b are 12.
Hence option (1) is correct.

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