If `c` is positive and `2a x^2+3b x+5c=0` does not have aby real roots, then prove that `2a-3b+5b>0.`

If c is positive and 2a x^2+3b x+5c=0 does not have any real roots, then prove that 2a-3b+5b>0.

If c is positive and 2ax^(2)+3bx+5c=0 does not have aby real roots,then prove that 2a-3b+5b>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, c gt 0 and ax^2 + 2bx + 3c = 0 does not have any real roots then prove that: (i) 4a-4b + 3c gt 0 , (ii) a + 6b + 27c gt 0 , (iii) a + 2b + 6c gt 0

If c lt 0 and ax^2 + bx + c = 0 does not have any real roots then prove that: (i) a-b + c lt 0 , (ii) 9a +3b +c lt 0

If the equation a x^2+b x+c=0 has two positive and real roots, then prove that the equation a x^2+(b+6a)x+(c+3b)=0 has at least one positive real root.

If the equation a x^2+b x+c=0 has two positive and real roots, then prove that the equation a x^2+(b+6a)x+(c+3b)=0 has at least one positive real root.

Given that a x^2+b x+c=0 has no real roots and a+b+c 0 d. c=0

Given that a x^2+b x+c=0 has no real roots and a+b+c 0 d. c=0

If quadratic equation ax^2+bx+c=0 does not have real roots, then which of the following may be false (a) a(a-b+c) gt 0 (b) c(a- b+c)>0 e) b(a- b+c) gt 0 (d) a +b+c) (a-b+c)gt0