If ax^2 + bx + c = 0 has real and distinct ro | vedclass

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

Question

(B) Given the quadratic equation $ax^2 + bx + c = 0$ with $a > 0, b < 0, c < 0$.Sum of roots ($S$.$O$.$R$.) $= \alpha + \beta = -\frac{b}{a}$. Since $

Vedclass · Accepted Answer

$0 < |\alpha| < \beta$

Vedclass · Answer

(B) Given the quadratic equation $ax^2 + bx + c = 0$ with $a > 0, b Sum of roots ($S$.$O$.$R$.) $= \alpha + \beta = -\frac{b}{a}$. Since $b 0$,$-\frac{b}{a} > 0$,so $\alpha + \beta > 0$.Product of roots ($P$.$O$.$R$.) $= \alpha \beta = \frac{c}{a}$. Since $c 0$,$\frac{c}{a} Since the product of the roots is negative,one root must be positive and the other negative. Let $\alpha 0$.Given $\alpha + \beta > 0$,the positive root must have a larger absolute value than the negative root. Thus,$|\beta| > |\alpha|$.Since $\beta > 0$,we have $\beta > |\alpha|$.Therefore,$0 < |\alpha| < \beta$.

If $ax^2 + bx + c = 0$ has real and distinct roots,$\alpha$ and $\beta$ $(\beta > \alpha)$. Further $a > 0, b < 0$ and $c < 0$ then :-

Similar Questions

If the roots of the equation $x^2 + px + q = 0$ differ by $1$,then:

The roots of the equation $4^x - 3 \cdot 2^{x+2} + 32 = 0$ are

$I. \quad p^{2}-18 p+77=0$
$II. \quad 3 q^{2}-25 q+28=0$
$Quantity \, 1$: Value of $p$
$Quantity \, 2$: Value of $q$

If one root of $ax^2 + bx + c = 0$ is the square of the other,then the value of $b^3 + ac^2 + a^2c$ is

If the difference between the roots of the equation $x^2 + ax + 1 = 0$ is less than $\sqrt{5}$,then the set of possible values of $a$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module