if b2 = 4ac for the eqn ax4 + bx2 + c =0 then all the root of the - Maths - Complex Numbers and Quadratic Equations

Question

if b2 >= 4ac for the eqn ax4 + bx2 + c =0 then all the root of the eqnwill be real if ? ans i) b < 0 , a > 0 , c > 0 ii) b > 0 , a < 0, c < 0

Rishabh Mittal · Accepted Answer

ax4+bx2+c=0 1Let x2=t at2+bt+c=0 2For equation 1 to have real roots , roots of equation 2 should be real and positive For roots of equation 2 to be real and positive -ba>0 , ca>0 and b2-4ac≥0For -ba>0 , b and a should have opposite signs For ca>0 , c and a must have same signs b2-4ac≥0 GivenTherefore,If a>0 then b<0 and c>0 Whena<0 then b>0 and c<0

if b2 >= 4ac for the eqn ax4 + bx2 + c =0 then all the root of the eqnwill be real if ............. ? ans. i) b < 0 , a > 0 , c > 0 ii) b > 0 , a < 0, c < 0

if b² >= 4ac for the eqn ax⁴ + bx² + c =0 then all the root of the eqnwill be real if ............. ?

ans.
i) b < 0 , a > 0 , c > 0

ii) b > 0 , a < 0, c < 0