Question

the real roots of x(3x-1)(x2+9)=0 are

Answer 1

Answer:

An equation is said to have two distinct and real roots if the discriminant b2−4ac>0

Case (i): For equation: 2x2−32x+49=0.

Here a=2,b=−32,c=49

The discrimant is (−32)2−4(2)(49)=18−18=0

Hence this equation has equal real roots

Case (ii): For equation: x2+x−5=0.

Here a=1,b=1,c=−5

The discrimant is 12−4(1)(−5)=1+20=21>0

Hence this equation has two distinct real roots

Case (iii): For equation: x2+3x+22=0.

Here a=1,b=3,c=22

The discrimant is 32−4(1)(22)=9−82<0

Hence this equation has no real roots

Case (iv): For equation: 5x2−3x+1=0.

Here a=5,b=−3,c=1

The discrimant is (−3)2−4(5)(1)=9−20<0

Hence this equation has no real roots