Discriminant

Q. root 2 + root 3/3 root 2- 2 root 3 = a-b root 6. find the values of a and b

Q.

Question 10
Which of the following equations has no real roots?
(A) $x^2-4x+3\sqrt{2}=0$
(B) $x^2+4x-3\sqrt{2}=0$
(C) $x^2-4x-3\sqrt{2}=0$
(D) $3x^2-4\sqrt{3}x+4=0$

Q.

If $x=0.\overline{17}$, then which of the following statements are true?

(i) $100x=17.\overline{17}$
(ii) $100x-x=16.\overline{17}$
(iii) $99x=17$

1. (i) and (iii)
2. (i), (ii) and (iii)
3. (i) only
4. (i) and (ii)

Q.

If the equation $x^2-m(2x-8)-15=0$ has equal roots then $m=?$

1. $3,-5$

2. $-3,5$

3. $3,5$

4. $-3,-5$

Q. The zeros and roots of a quadratic equation are _____.

1. same
2. unequal
3. different
4. dissimilar

Q.

If the discriminant of the quadratic equation 4x² + px + 25 = 0; is 0, then find the value of p. Given $p>0.$

1. 10

2. 20

3. 30

4. -20

Q.

Class mark of a class interval 30-38 is

1. 38

2. 36

3. 34

4. 30

Q. Find the value of $x$ if
$\left(\frac{625}{81}\right)\times (\frac{125}{27}{)}^x=(\frac{25}{9}{)}^8$

1. 4
2. 5
3. -3
4. -4

Q. Find the sum of roots and product of roots respectively for $2x^2+x-5=0$

1. $-\frac{1}{2},\frac{5}{2}$
2. 2, 5
3. $-\frac{1}{2},-\frac{5}{2}$
4. $-\frac{1}{2},\frac{5}{2}$

Q.

If roots of polynomial ax^3+3bx^2+3cx+d are in A.p. prove that 2b^3-3abc+a^2d=0

Q.

Find the value of $k$ for which the quadratic equation $(k+4)x^2+(k+1)x+1=0$ has equal roots.

Q. Which of the following is/are a polynomial?

1. $2y+\frac{2}{y}$
2. $3\sqrt{x}+x^2$
3. $x+y$
4. $xy$

Q. If $(x-3)$ is a factor of $p\left(x\right)$ , find the value of $k$ , Where $p\left(x\right)=$$x^2-k^{2}x+k$

Q. Find the value of discriminant for the following equation.

Q. One of the two students while solving a quadratic equation in $x$ copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term and coefficient of $x^2$ correctly as -6 and 1 respectively. The correct roots are

1. $3,-2$
2. $-3,2$
3. $-6,-1$
4. $6,-1$

Q. A quadratic equation $x^2+kx+2=0$ has one of its roots as $2$. What is the value of $k$ ?

1. $1$
2. $3$
3. $-3$
4. $-2$

Q. If $\alpha ,\beta$ are the roots of $a{x}^2+bx+c=0$ and $\alpha +\beta ,{\alpha }^2+{\beta }^2,{\alpha }^3+{\beta }^3$ are in G.P., where $△=b^2-4ac$, then

1. 
2. 
3. 
4. 

Q. If $a+b+c=12$ and $a^2+b^2+c^2=50$, then ab + bc + ca = .

1. $88$
2. $47$
3. $84$
4. $94$

Q. In the figure, given, below, AD $\perp$ BC. then, $c^2=a^2+b^2-2ax.$
If the above statement is true then mention answer as 1, else mention 0 if false

Q. Find the value of discriminant for the following equation.

Q. If 2/√3 and -2/√3 are roots of polynomial 3x^4-12x^3+5x^2+16x-12, thenfind the other two roots.

Q. All the 3 sides of a right triangle are integers and one side has a length $11$ units. Area of the triangle in square units lies between

1. $1$ and $100$
2. More than $300$
3. $100$ and $200$
4. $200$ and $300$

Q. if x = 1/3 - root 5. then find the value of root x + 1/root x

Q. Product of real roots of the equation $t^2{x}^2+|x|+9=0$

1. is always positve
2. is always negative
3. does not exists
4. none of these

Q. Find the nature of roots x2+X-(a+2)(a+1)=0

Q. root 2 + root 3/3 root 2- 2 root 3 = a-b root 6. find the values of a and b

Q. The product of $\sqrt{x}+2\sqrt{y}$ with its conjugate is?

1. $x-2y$
2. $x+4y$
3. $x-4y$
4. $x+2y$

Q. Find the discriminant of the equation $3x^2-2x+\frac{1}{3}=0$.

Q. Which of the following is not a polynomial?

1. $x^3-1$
2. $4x^2+2x+1$
3. $y+\frac{3}{y}$
4. $y^2+5y+1$

Q. If $x+y=\sqrt{22}$ and $x-y=\sqrt{10}$, then $xy=$

1. $\sqrt{22\times 10}$
2. $3$
3. $16$
4. $55$
5. $12$