If $p, q \in \mathbf{R}$ and $2+\sqrt{3} i$ a foot of $x^2+p x+$ $q=0$, then

JEE MATHEMATICS MCQ: QUADRATIC EQUATIONS

1 Easy

1 of 1

Application +4 | -1

p, q \in \mathbf{R}

and

2+\sqrt{3} i

a foot of

x^2+p x+

q=0

, then

View answer and explanation

Correct option: B

p=-4, q=7

Option B (p=-4, q=7) is correct because if

2 + \sqrt{3}i

is a root, then its conjugate

2 - \sqrt{3}i

is also a root, and we can find p and q using Vieta's formulas.

Practice All Chapter MCQs →

\log _7 \log _5(\sqrt{x+5}+\sqrt{x})=0

\alpha ,\beta

{x^2} - 3x + a = 0,a \in R

\alpha < 1 < \beta ,

\alpha ,\;\beta

{x^2} - px + q = 0

{\alpha _1},{\beta _1}

{x^2} - qx + p = 0,

\frac{1}{{{\alpha _1}\beta }} + \frac{1}{{\alpha {\beta _1}}}\mathrm{and}\;\frac{1}{{\alpha {\alpha _1}}} + \frac{1}{{\beta {\beta _1}}},

{x^2} + 4ax + 2 > 0

x

a

f\left( x \right) = a{x^2} + bx + c\;

\;f\left( { - 1} \right) < 1,f\left( 1 \right) > - 1,f\left( 3 \right) < - 4\;

\;a \ne 0,

9{x^2} - 18\left| x \right| + 5 = 0

f\left( x \right) = \log \left( {{x^2} - x - 2} \right)