Question

The zeroes of the quadratic polynomial 3x²+5x+12 are
a) both positive
b) both negative
c) one positive and one negative
d) equal in magnitude, but opposite in signs ​

Answer 1

Roots of the quadratic equation ax

2

+bx+c=0 are imaginary.

⇒b

2

−4ac<0 -----(1)

Now, for the expression a

2

x

2

+abx+ac,

Δ=a

2

b

2

−4a

3

c=a

2

(b

2

−4ac)<0 from (1)

Since, discriminant value is less than zero, coefficient of x

2

and expression always have same sign.

∴a

2

x

2

+abx+ac>0

Hence, option A.