Question

If one root of x^2+px+12=0 is 4.While the equation x^2+px+q=0 has equal roots then q=

Answer 1

Answer:

Step-by-step explanation:

Given \: 4 \: is \: one \: root \: of \: quadratic\\equation \: x^{2}+px+12 = 0  

/* Substitute x = 4 in the equation, we get

\implies 4^{2} + p\times 4 + 12 = 0

/* Divide each term by 4, we get

\implies 4 + p + 3 = 0  

\implies p + 7 = 0  

\implies p = -7 \: --(1)

Now,

Compare x^{2}+px+q = 0 \: with \:ax^{2}+bx+c=0,\\we \:get  

a = 1 , \: b = p , \: c = q  

Discreminant (D) = 0  

/* Given roots are equal */

b^{2} - 4ac = 0  

\implies p^{2} - 4\times 1 \times q = 0  

\implies (-7)^{2} - 4q = 0 \: [ from \: (1)]

\implies 49 = 4q  

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