Question

Which of the following statements is/are true for the given quadratic equations?

• A. $x^2-7x+12=0$ has roots of the same sign
• B. $x^2-7x+12=0$ has roots of different sign
• C. $x^2+5x+6=0$ has positive roots
• D. $-3x^2-x+2=0$ has roots of the opposite sign

Answer 1

Answer: (A), (D)

$-3x^2-x+2=0$ has roots of the opposite sign

$\left(i\right)x^2+5x+6=0$
Here $a,b,c$ are of the same sign
$\Rightarrow$ The roots will be negative

$\left(ii\right)-3x^2-x+2=0$
Here $a.c=(-3)\left(2\right)=-6<0$
$\Rightarrow$ The roots will be of opposite sign

$\left(iii\right)x^2-7x+12=0$
Here $a.c=\left(1\right)\left(12\right)=12>0$
$\Rightarrow$ The roots will be of the same sign