If 2a+3b+6c = 0, then show that the equation `a x^2 + bx + c = 0` has atleast one real root between 0 to 1.

the quadratic equation 3ax^2 +2bx+c=0 has atleast one root between 0 and 1, if

Statement 1: If 27 a+9b+3c+d=0, then the equation f(x)=4a x^3+3b x^2+2c x+d=0 has at least one real root lying between (0,3)dot Statement 2: If f(x) is continuous in [a,b], derivable in (a , b) such that f(a)=f(b), then there exists at least one point c in (a , b) such that f^(prime)(c)=0.

If a,b,c in R and a+b+c=0, then the quadratic equation 3ax^2+2bx+c=0 has (a) at least one root in [0, 1] (b) at least one root in [1,2] (c) at least one root in [3/2, 2] (d) none of these

If b^2<2a c , then prove that a x^3+b x^2+c x+d=0 has exactly one real root.

Let a, b, c in R with a gt 0 such that the equation ax^(2) + bcx + b^(3) + c^(3) - 4abc = 0 has non-real roots. If P(x) = ax^(2) + bx + c and Q(x) = ax^(2) + cx + b , then

If -i + 2 is one root of the equation ax^2 - bx + c = 0 , then the other root is …………

Let a gt 0, b gt 0, c gt 0 . Then both the roots of the equation ax^2+ bx + c = 0 are

The equation 4ax^2 + 3bx + 2c = 0 where a, b, c are real and a+b+c = 0 has

Without actually solving show that the equation x^(4)+2x^(3)-2=0 has only one real root in the interval (0,1) .

If 2a+3b+6c=0, then prove that at least one root of the equation a x^2+b x+c=0 lies in the interval (0,1).