Class 11Mathematics4-2.Quadratic Equations and InequationsSolution of quadratic equations and Nature of roots
MediumIf ${x_1}, {x_2}, {x_3}$ are distinct roots of the equation $ax^2 + bx + c = 0$,then:
- A$a = b = 0, c \in R$
- B$a = c = 0, b \in R$
- C$b^2 - 4ac \ge 0$
- D$a = b = c = 0$
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Similar Questions
The real root of the equation $x^{3}-6x+9=0$ is
If $x^2 - 3x + 2$ is a factor of $x^4 - px^2 + q$,then $(p, q) = $
MediumIIT 1974
View SolutionFor how many values of $a$ does the equation $(a^2 - 3a + 2)x^2 + (a^2 - 4)x + a^2 - a - 2 = 0$ become a linear equation?
Medium
View SolutionWith respect to the roots of the equation $3x^3 + bx^2 + bx + 3 = 0$,match the items of List-$I$ with those of List-$II$.
List-$I$ List-$II$ $A$. All the roots are negative $I$. $(b - 3)^2 = 36 + P^2$ for $P \in R$ $B$. Two roots are complex $II$. $-3 < b < 9$ $C$. Two roots are positive $III$. $b \in (-\infty, -3) \cup (9, \infty)$ $D$. All roots are real and distinct $IV$. $b = 9$ $V$. $b = -3$
| List-$I$ | List-$II$ |
| $A$. All the roots are negative | $I$. $(b - 3)^2 = 36 + P^2$ for $P \in R$ |
| $B$. Two roots are complex | $II$. $-3 < b < 9$ |
| $C$. Two roots are positive | $III$. $b \in (-\infty, -3) \cup (9, \infty)$ |
| $D$. All roots are real and distinct | $IV$. $b = 9$ |
| $V$. $b = -3$ |
If $\sqrt{3x^2 - 7x - 30} + \sqrt{2x^2 - 7x - 5} = x + 5$,then $x = \dots$
Medium
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