CAT 1994 | Question: 62

Question

If one root of $x^{2} + px + 12 = 0$ is $4$, while the equation $x^{2} + px + q = 0$ has equal roots, then the value of $q$ is:

• A. $49/4$
• B. $4/49$
• C. $4$
• D. $\frac{1}{4}$

Answer 1

We know :

In quadratic equation :  ax² + bx +  c = 0

a) Sum of roots  =  (-b/a)

b) Product of roots  =  (c/a)

Hence for the equation : x² +px + 12 = 0 , we are given one root as 4 and c = 12 which is product of the two roots.

Thus the other root  =  12 / 4  =  3

==> Sum of roots    =  4 + 3  =  7    ==> -p  =  7  ==> p = -7

Now for the other given equation :   x² +px + q = 0  , which can be now written as : x²  - 7x + q = 0

It is given that this equation has equal roots . 

We know : 

For equal roots , we have discriminant  " b² - 4ac = 0" 

So here we have :

        49 - 4q = 0 

==>  q         =  49 / 4

Hence A) should be the correct option.

Answer 2

If one root of $x^{2}+px+12=0$ is $4$  and $x^{2}+px+q=0$ has equal roots

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Answer 3

if one root is given then we the root must satisfy its equation so 16 + 4p +12 = 0 so p = -7

Now if second equation have equal roots when b² -4ac = 0 so p²-4q = 0  put p = -7  then q = 49/4 

hence option A