If the equaiton ax^2+bx+c=0 where a,b,c in R have non-real roots then-
If ax^2+bx+c =0 and cx^2+bx+a =0 (a,b,cinR) have a common non-real roots,then
if ax^2+bx+c = 0 has imaginary roots and a+c lt b then prove that 4a+c lt 2b
If ax^(2)+bx+c=0 , a ne 0 , a , b , c in R has distinct real roots in (1,2) , then a and 5a+2b+c have (a) same sign (b) opposite sign (c) not determined (d) none of these
If the equation a x^2+b x+c=0(a >0) has two real roots alphaa n dbeta such that alphalt-2 and betagt2, then which of the following statements is/are true? (a) a-|b|+c<0 (b) clt0,b^2-4a cgt0 (c) 4a-2|b|+c<0 (d) 9a-3|b|+c<0
Let a, b, c be three real numbers such that a + 2b + 4c = 0. Then the equation ax^(2) + bx + c=0
If 2a+3b+6c=0 (a,b,cinR) , then the quadratic equation ax^2+bx+c =0 has
If ax^(2)+(b-c)x+a-b-c=0 has unequal real roots for all c epsilon R , then (i) b a > 0
If (cgt 0) and 2ax^2+3bx+5c =0 does not have any real roots, then prove that 2a-3b+5c gt 0.
If a,b,c in R : a ne 0 and the quadratic equation ax^2+bx+c =0 has no real root, then show that (a+b+c)c gt 0
CHHAYA PUBLICATION-QUADRATIC EQUATIONS-Sample Question for Competitive Exams (Assertion- Reason Type)
