True or false The equation`2x^2+3x+1=0` has an irrational root.

By using the method of completing the square, show that the equation 4x^2+3x+5=0 has no real roots.

Prove that both the roots of the equation x^(2)-x-3=0 are irrational.

Which of the following is not true for equation x^(2)log8-xlog5=2(log2)-x (A) equation has one integral root (B) equation has no irrational roots (C) equation has rational roots (D) none of these

Find the condition if the equation 3x^2+4a x+b=0 has at least one root in (0,1)dot

Find the condition if the equation 3x^2+4a x+b=0 has at least one root in (0,1)dot

Find the value of k for which the equation 3x^(2)-6x+k=0 has distinct and real root.

If p and q are odd integers, then the equation x^2+2px+2q=0 (A) has no integral root (B) has no rational root (C) has no irrational root (D) has no imaginary root

The roots of the equations x ^2−x−3=0 are a. imaginary b. rational. c. irrational d. none of these.

If alpha, beta, gamma, are the roots of the equation x^(3)+3x-1=0, then equation whose roots are alpha^(2),beta^(2),gamma^(2) is

Statement-1: Let a,b,c be non zero real numbers and f(x)=ax^2+bx+c satisfying int_0^1 (1+cos^8x)f(x)dx=int_0^2(1+cos^8x)f(x)dx then the equation f(x)=0 has at least one root in (0,2) .Statement-2: If int_a^b g(x)dx vanishes and g(x) is continuous then the equation g(x)=0 has at least one real root in (a,b) . (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true