Question

if one root of the equation x2 + px + 12=0 is 4 , while the equation x2 + px + q =0 has equal roots, the value of q is

a) 49/4

b) 4/49

c) 4

d) none of these

Answer 1

Answer:

Option ( a ) is correct

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 */

$b^{2} - 4ac = 0$

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

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

$\implies 49 = 4q$

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

Therefore,

Option ( a ) is correct

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Answer 2

Answer:

so the answer is :

q= 49/4

hope that it's helpful to you

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