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Explore popular questions from Quadratic Equations for SSC. This collection covers Quadratic Equations previous year SSC questions hand picked by experienced teachers.

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Quadratic Equations

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Q 1. If {tex}a , b , c {/tex} are three natural numbers such that {tex} c {/tex} is a factor of {tex}ab{/tex} and {tex} c {/tex} is coprimes to {tex}a{/tex} then

A

{tex} { b } {/tex} is a factor of {tex} { c } {/tex}

{tex}c {/tex} is a factor of {tex}b {/tex}

C

{tex}a {/tex} is a factor of {tex}b {/tex}

D

{tex}b {/tex} is a factor of {tex}a {/tex}

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Q 2. The graph of the polynomial {tex} f ( x ) = a x ^ { 2 } + b x + c {/tex} is as shown in fig, then which of the following is/are true:-

A

{tex} \mathrm { a } > 0 , \mathrm { b } > 0 , \mathrm { c } < 0 {/tex}

B

{tex} \mathrm { a } < 0 , \mathrm { b } > 0 , \mathrm { c } > 0 {/tex}

{tex} \mathrm { a } < 0 , \mathrm { b } > 0 , \mathrm { c } < 0 {/tex}

D

{tex} \mathrm { a } < 0 , \mathrm { b } < 0 , \mathrm { c } < 0 {/tex}

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Q 3. {tex} x^{2}-x-12=0; y^{2}+5y+6=0 {/tex}

A

If {tex} x > y {/tex}

If {tex} x\ge y {/tex}

C

lf {tex} x < y {/tex}

D

If {tex} x \le y {/tex}

Explanation

{tex} x^{2} - x - 12 = 0 {/tex}
={tex} x^{2} - 4x + 3x - 12 = 0 {/tex}
={tex} x \left(x-4\right) + 3 \left(x-4\right) = 0 {/tex}
={tex} \left(x-4\right) \left(x+3\right) = 0 {/tex}
Therefore, {tex}x{/tex} = -3, 4
and {tex} y^{2} + 5y + 6 = 0 {/tex}
={tex} y^{2} + 3y + 2y + 6 = 0 {/tex}
={tex} y \left(y+3\right) + 2 \left(y+3\right) = 0 {/tex}
={tex} \left(y + 3\right) \left(y - 3\right) = 0 {/tex}
= {tex}y{/tex} = -3, -2
Therefore, {tex} x \ge y {/tex}
[because {tex}x{/tex} = -3 and {tex}y{/tex} = -3, so {tex}x{/tex} = {tex}y{/tex} and {tex}x{/tex} = 4 and {tex}y{/tex} = -2, hence {tex}x{/tex} > {tex}y{/tex}]

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Q 4. If {tex} \frac { x + a } { x - a } - \frac { x - b } { x + b } = \frac { 2 ( a + b ) } { x } , {/tex} then {tex} x = {/tex}

A

{tex} \frac { a } { a - b } {/tex}

B

{tex} \frac { b } { a - b } {/tex}

C

{tex} \frac { a b } { a - b } {/tex}

{tex} \frac { a b } { b - a } {/tex}