NIMCET 2007 — Mathematics PYQ

Step 1: Find the value of $p$

Since $4$ is a root of the first equation $x^2+px+12=0$, it must satisfy the equation. Substitute $x=4$ into the equation:

$$(4{)}^2+p(4)+12=0$$

$$16+4p+12=0$$

$$4p+28=0$$

$$4p=-28$$

$$p=-7$$

Step 2: Substitute $p$ into the second equation

Now substitute $p=-7$ into the second quadratic equation $x^2+px+q=0$:

$$x^2-7x+q=0$$

Step 3: Use the condition for equal roots to find $q$

For a quadratic equation $a{x}^2+bx+c=0$ to have equal roots, its discriminant ($D$) must be equal to zero ($D=0$).

$$D=b^2-4ac=0$$

Comparing $x^2-7x+q=0$ with the standard form, we get:

• $a=1$

• $b=-7$

• $c=q$

Substitute these values into the discriminant formula:

$$(-7{)}^2-4(1)(q)=0$$

$$49-4q=0$$

$$4q=49$$

$$q=\frac{49}{4}$$

Conclusion

The value of $q$ is $\frac{49}{4}$.

Therefore, the correct option is (c).