1 Marks Question

Question 11 Mark

(a) Find the nature of the roots of the quadratic equation $x^2-5 x+9=0$.
(b) Write a quadratic equation with roots -3 and 5.

Answer

(a) imaginary (b) $x^2-2 x-15=0$

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Question 21 Mark

Solve the quadratic equation $2 x^2-5 x-1=0$ for $x$.

Answer

$\frac{5 \pm \sqrt{33}}{4}$

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Question 31 Mark

Find the value of k for which the roots of the equation $3 x^2-10 x+k=0$ are reciprocal of each other.

Answer

k = 3

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Question 41 Mark

For what value of k, the roots of the equation $x^2+4 x+k=0$ are real?

Answer

$k \leq 4$

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Question 51 Mark

If x = 3 is one root of the quadratic equation $x^2-2 k x-6=0$, then find the value of k.

Answer

$k=\frac{1}{2}$

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Question 61 Mark

If $x=\frac{-1}{2}$, is a solution of the quadratic equation $3 x^2+2 k x-3=0$, find the value of k.

Answer

$-\frac{9}{4}$

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Question 71 Mark

Find the discriminant of the quadratic equation $3 \sqrt{3} x^2+10 x+\sqrt{3}=0$

Answer

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Question 81 Mark

Show that x =-2 is a solution of $3 x^2+13 x+14=0$.

Answer

self

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Question 91 Mark

Show that x =-3 is a solution of $x^2+6 x+9=0$.

Answer

self

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Question 101 Mark

Write the set of values of k for which the quadratic equation has $2 x^2+k x-8=0$ has real roots.

Answer

All real values

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Question 111 Mark

Is there any real value of 'a' for which the equation $x^2+2 x+\left(a^2+1\right)=0$ has real roots?

Answer

Yes, a = 0

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Question 121 Mark

Write the set of values of 'a' for which the equation $x^2+a x-1=0$ has real roots.

Answer

All real values

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Question 131 Mark

Write the condition to be satisfied for which equations $a x^2+2 b x+c=0$ and $b x^2-2 \sqrt{a c} x+b=0$ have equal roots.

Answer

$b^2=a c$

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Question 141 Mark

Write the value of $\lambda$ for which $x^2+4 x+\lambda$ is a perfect square.

Answer

$\lambda=4$

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Question 151 Mark

Write the sum of real roots of the equation $x^2+|x|-6=0$.

Answer

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Question 161 Mark

Write the number of real roots of the equation $x^2+3|x|+2=0$.

Answer

No real root

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Question 171 Mark

If $1+\sqrt{2}$ is a root of a quadratic equation with rational coefficients, write its other root.

Answer

$1-\sqrt{2}$

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Question 181 Mark

Write a quadratic polynomial, sum of whose zeros is $2 \sqrt{3}$ and their product is 2.

Answer

$f(x)=k\left(x^2-2 \sqrt{3} x+2\right)$,where k is any real number

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Question 191 Mark

What is the nature of roots of the quadratic equation $4 x^2-12 x-9=0 ?$

Answer

Real and distinct

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Question 201 Mark

Write the value of k for which the quadratic equation $x^2-k x+4=0$ has equal roots.

Answer

k=±4

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