Quadratic Equation for the Given Roots

Q.

$\text{If}\alpha \text{and}\beta \text{are zeroes of the polynomial}2x^2+5x+1,\text{then find the value of}\alpha +\beta +\alpha \beta .$

Q. Which of the following equations has the roots 7 and 8?

1. $x^2-17x+2=0$
2. $x^2-15x+56=0$
3. $x^2-19x+1=0$
4. $x^2-x+19=0$

Q. Which of the following equations has the roots 2 and 3?

1. $x^2-6x+2=0$
2. $x^2-5x+6=0$
3. $x^2-4x+2=0$
4. $x^2-6x+7=0$

Q. Which of the following equations has the roots 3 and 4?

1. $x^2-6x+2=0$
2. $x^2-6x+9=0$
3. $x^2-8x+2=0$
4. $x^2-7x+12=0$

Q.

Find the sum and the product of the roots of the following equations 3$x^2$ + 6x + 9 = 0

Q. Arrange the following equations based on the ascending order of sum of their roots.(Top to bottom direction)

1. $x^2-6x+8=0$
2. $x^2-4x+4=0$
3. $x^2-8x+16=0$
4. $x^2-2x+1=0$

Q. Which of the following equations has the roots 1 and 2?

1. $x^2-4x+2=0$
2. $x^2-6x+2=0$
3. $x^2-3x+2=0$
4. $x^2-3x+8=0$

Q. Find the values of k for which the following equation has equal roots: [4 MARKS]

$(k-12)x^2+2(k-12)x+2=0$

Q.

1. $b>0$
2. $b<0$
3. $a>0$
4. $a<0$

Q. Find the discriminant of each of the following equations:
$2x^2-7x+6=0$

Q. If in an A.P, $a_9=0,a_{19}=k$, then $a_{29}$ is

1. $k^2$
2. $10k$
3. $9k$
4. $2k$

Q. Say true or false.

1. True
2. False

Q. Find the discriminant of each of the following equations:
$3x^2-2x+8=0$

Q. Find the values of k for which the following equation has equal roots: [4 MARKS]

$(k-12)x^2+2(k-12)x+2=0$