Discriminant

Q.

The roots of the quadratic equation √3x² - 2√2x - 2√3 = 0 are:

1. 

2. 

3. 

4. 

Q. If one of the zero of x²-3kx+4k is twice the other. Find the value of k.

Q.

Find the values of $a$ and $b$in $\frac{3+\sqrt{2}}{3-\sqrt{2}}=a+b\sqrt{2}$.

Q. Find the roots of the quadratic equation $2x^2+x–6=0$ by factorisation.

1. $x=-2,\frac{2}{3}$
2. $x=2,\frac{2}{3}$
3. $x=2,\frac{3}{2}$
4. $x=-2,\frac{3}{2}$

Q.

Rationalize the denominator$\frac{3-2\sqrt{2}}{3+2\sqrt{2}}$.

Q. Solve the following pair of linear equations:
$\frac{x}{2}+\frac{2y}{3}=-1$ and $x-\frac{y}{3}=3$

1. 2, -3
2. -3, 2
3. 4, -3
4. 2, 4

Q.

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them.

$2x^2-3x+5=0$.

Q.

Find the values of p for which the quadratic equation $(p+1)x^2-6(p+1)x+3(p+9)=0,p\ne -1$ has equal roots. Hence, find the roots of the equation.

Q.

If $a{x}^2+bx+c=0$ and $2x^2+3x+4=0$ have a common root, where $a,b,c\in N$(set of natural numbers), then the least value of $a+b+c$ is

1. $13$

2. $11$

3. $7$

4. $9$

Q.

Rationalize the denominator$\frac{16}{\sqrt{41}-5}$.

Q.

State true or false. The discriminant for general quadratic equation $a{x}^2+bx+c=0$ is $b^2–4ac$.

1. True

2. False

Q.

The roots of equation, x² + 1 = 0, are

1. (1, 1)
2. (1, -1)
3. (1, 2)
4. Has no roots

Q. The discriminant of x^2 + 3x + 1 = 0 is

1. 6
2. 5
3. 10
4. 8

Q.

$\sqrt{11\sqrt{11\sqrt{11...4\mathrm{terms}}}}=()?$

1. $\sqrt[16]{{11}^{14}}$

2. $\sqrt[16]{{11}^4}$

3. $11$

4. $\sqrt[16]{{11}^{15}}$

Q. ($a{x}^2+bx+c=0$) is the standard form of a quadratic equation.

1. False
2. True

Q.

The roots of the quadratic equation $x^2$+5x-14=0 is

1. 2, -7

2. -2, -7

3. -2, 7

4. 2, 7

Q.

If the equation $x^2+2(k+2)x+9k=0$ has real equal roots, then values of $k$ are ____

1. $–1and5$

2. $1and–5$

3. $–1and–4$

4. $1and4$

Q.

Alpha and beta are roots of this equation; 4_x²-7x+3=0 then find alpha cube + beta cube and also find 1 upon alpha square + 1 upon beta square

Q.

The solution for the pair of linear equations

x + 2y = 5 and 7x + 3y = 13 is (2, 1).

1. True

2. False

Q. Find the roots of the quadratic equation $x^2+4x-12=0.$

1. 6 and - 2
2. - 6 and 2
3. - 4 and 3
4. 3 and 4

Q.

If alpha and beta are zero of p(x)=x²+x-1 then find alpha square beta+alpha beta square

Q. Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.
$x^2+2(m-1)x+(m+5)=0$
[4 MARKS]

Q.

The number of integers $n(<20)$ for which $n^2-3n+3$ is a perfect square is:

1. $0$

2. $1$

3. $2$

4. $3$

Q. The equation $k^2{x}^2+kx+1=0$ has ____

1. one real root
2. two real roots
3. no real roots
4. equal roots

Q.

Find the discriminant of each of the following equations :
(i) $2x^2-7x+6=0$ (ii) $3x^2-2x+8=0$
(iii) $2x^2-5\sqrt{2}x+4=0$ (iv) $\sqrt{3}{x}^2+2\sqrt{2}x-2\sqrt{3}=0$
(v) $(x-1)(2x-1)=0$ (vi) $1-x=2x^2$

Q. The discriminant of the equation $2x^2-5x-2=0$ is

1. 41

Q.

Show that:$(\mathrm{a}-\mathrm{b})(\mathrm{a}+\mathrm{b})+(\mathrm{b}-\mathrm{c})(\mathrm{b}+\mathrm{c})+(\mathrm{c}-\mathrm{a})(\mathrm{c}+\mathrm{a})=0$

Q. Without solving the following quadratic equation, find the value of 'p' for which the given equation has real and equal roots:
$x^2+(p-3)x+p=0$.

Q.

Let $f:(0,\infty )\to R$ be a differentiable function such that
$f^{\prime }\left(x\right)=2-\frac{f\left(x\right)}{x}$ for all $xϵ(0,\infty )$ and $f\left(1\right)\ne 1$. Then

1. $\underset{x\to 0^{+}}{lim}{f}^{\prime }\left(\frac{1}{x}\right)=1$

2. $\underset{x\to 0^{+}}{lim}xf\left(\frac{1}{x}\right)=2$

3. $\underset{x\to 0^{+}}{lim}{x}^2{f}^{\prime }x=0$

4. $|f\left(x\right)|\le 2$ for all $xϵ(0,2)$

Q.

If 3 is root of the quadratic equation $x^2-x+k=0$, find the value of p so that the roots of the equation $x^2+k(2x+k+2)+p=0$ are equal.