If the roots of the equation x^2 - 2cx + ab = | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given the equation $x^2 - 2cx + ab = 0$ has real and unequal roots,its discriminant $D_1 > 0$. $D_1 = (-2c)^2 - 4(1)(ab) = 4c^2 - 4ab > 0$,which i

Vedclass · Accepted Answer

imaginary

Vedclass · Answer

(B) Given the equation $x^2 - 2cx + ab = 0$ has real and unequal roots,its discriminant $D_1 > 0$. $D_1 = (-2c)^2 - 4(1)(ab) = 4c^2 - 4ab > 0$,which implies $c^2 > ab$. Now,consider the equation $x^2 - 2(a + b)x + a^2 + b^2 + 2c^2 = 0$. The discriminant $D_2$ of this equation is: $D_2 = [-2(a + b)]^2 - 4(1)(a^2 + b^2 + 2c^2)$ $D_2 = 4(a^2 + 2ab + b^2) - 4a^2 - 4b^2 - 8c^2$ $D_2 = 4a^2 + 8ab + 4b^2 - 4a^2 - 4b^2 - 8c^2$ $D_2 = 8ab - 8c^2 = 8(ab - c^2)$. Since $c^2 > ab$,it follows that $ab - c^2 Therefore,$D_2 Since the discriminant is negative,the roots of the equation are imaginary.

If the roots of the equation $x^2 - 2cx + ab = 0$ are real and unequal,then the roots of the equation $x^2 - 2(a + b)x + a^2 + b^2 + 2c^2 = 0$ are

Similar Questions

Let $S=\{1, 2, 3, \ldots, 100\}$. Suppose $b$ and $c$ are chosen at random from the set $S$. The probability that $4x^2+bx+c=0$ has equal roots is

If the expression $x^3+3x^2-9x+\lambda$ is of the form $(x-\alpha)^2(x-\beta)$,then the values of $\lambda$ are

For $x > 2$,the equation $\sqrt{x+2} - \sqrt{x-2} = \sqrt{4x-2}$ has

Let $a, b$ be non-zero real numbers. Which of the following statements about the quadratic equation $a x^2+(a+b) x+b=0$ is necessarily true?
$I$. It has at least one negative root.
$II$. It has at least one positive root.
$III$. Both its roots are real.

Solve the equation $21x^{2} - 28x + 10 = 0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module