Solving QE Using Quadratic Formula When D>0

Q.

Solve each of the following quadratic equations:
$12ab{x}^2-(9a^2-8b^2)x-6ab=0$

Q.

Solve the quadratic equationn $x^2-5x-10=0$ correct to 2 decimal places.

1. Roots are 6.93 and -1.53

2. Roots are 6.53 and -1.53

3. Roots are 6.53 and -1.59

4. Roots are 6.53 and -6.53

Q.

Find the roots of quadratic equation correct to two decimal places.
$2x^2-10x+5=0$

1. Roots are 4.44 and 0.59

2. Roots are 4.44 and 0.56

3. Roots are 8.44 and 0.56

4. Roots are 4.44 and 0.90

Q.

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$x^2+5x-(a^2+a-6)=0$

Q.

Evaluate the square root of $96$ in radical form

Q.

One of the real roots of the quadratic equation $3x^2-5x-2=0$ is :

1. $\frac{1}{3}$

2. $\pm \frac{1}{4}$

3. -3

4. 2

Q.

Using quadratic formula solve the following quadratic equation:

$p^2{x}^2+(p^2-q^2)x-q^2=0,p\ne 0$

1. The roots are : $\frac{q^2}{p^2},-1$

2. The roots are : $\frac{q^2}{p^2},-6$

3. The roots are : $\frac{2q^2}{p^2},-1$

4. The roots are : $\frac{q^2}{9p^2},-1$

Q.

The value of p for which the quadratic equation $2p{x}^2+6x+5=0$ has real and distinct roots is :

1. $\frac{1}{2}$

2. 1

3. 2

4. $\frac{9}{10}$

Q.

Solve each of the following quadratic equations:
$4x^2-2(a^2+b^2)x+a^2{b}^2=0$

Q. On Solving the following quadratic equation by factorization, the roots are :$\sqrt{6},-\sqrt{\frac{2}{3}}$
$\sqrt{3}{x}^2-2\sqrt{2x}-2\sqrt{3}=0$

1. true
2. false

Q. a) Solve the following equation and calculate the answer correct to two decimal places:
$x^2-5x-10=0$.

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

[6 MARKS]

Q.

Using quadratic formula, factorize the equation : [3 MARK]
$5x^2–10x+3=0$

Q.

Taylor purchased a rectangular plot of area $750m^2$. The length of the plot is 5 m more than its breadth. Find its length.

1. 88m & 24m

2. 34.6m & 11.20m

3. 32m &16m

4. 44.6m & 14.20m

Q. Prove that 2^1/2 is irrational.(Please explain step wise because I am a bit confused and I am not able to understand the logic behind it.)

Q.

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$x^2-(2b-1)x+(b^2-b-20)=0$

Q. Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula.

Q. Without solving the following quadratic equation, find the value of p for which the roots are equal:
$p{x}^2-4x+3=0$

Q.

In the following, determine whether the given quadratic equations have real roots and if so, find the roots. [3 MARKS]

$6x^2+x-2=0$

Q.

Solve the following quadratic equation using quadratic formula .

$9x^2-9(a+b)x+(2a^2+5ab+2b^2)=0$

1. The roots are $\frac{2a+b}{3}$ and $\frac{a+2b}{3}$

2. The roots are $\frac{5a+b}{3}$ and $\frac{a+2b}{3}$

3. The roots are $\frac{2a+b}{3}$ and $\frac{a-2b}{4}$

4. The roots are $\frac{2a+b}{3}$ and $\frac{a-2b}{3}$

Q. Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula.
(iv) $2x^2+x+4=0$

Q. A chessboard contains 64 equal squares and the area of each square is $6.25c{m}^2$. A border around the board is 2 cm wide. Find the length of the side of the chess board.

Q. Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula.
(iii) $4x^2+4\sqrt{3}x+3=0$

Q.

In the adjoining figure, find :

1. perimeter of the given figure
2. area of the given figure

Q. Solve the following quadratic equations by factorization method :
$\frac{x-a}{x-b}+\frac{x-b}{x-a}=\frac{a}{b}+\frac{b}{a}$

Q.

The roots of equation, x² + 2 = 0, are

1. (2, -2)
2. (2, 3)
3. (4, 4)
4. Not defined

Q. The equation $x^2+bx+c=0$ would have real roots if ____.

1. $b^2+4c\le 0$
2. $b^2-4c<0$
3. $b^2-4c\ge 0$
4. $b^2+4c>0$

Q.

A chessboard contains 64 equal squares and the area of each square is $6.25c{m}^2$. A border around the board is 2 cm wide. Find the length of the side of the chess board.

1. 36 cm

2. 24 cm

3. 16 cm

4. 32 cm

Q. The area of a rectangular plot is $528m^2$. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

Q. Which of the following satisfies the equation $a^2{b}^2{x}^2-b^{2}x-a^{2}x+1=0?$

1. $-\frac{1}{b^2}$
2. $\frac{1}{b^2}$
3. $\pm \frac{1}{b^2}$
4. $-\frac{1}{a^2}$

Q. Roots of the quadratic equation $4x^2+7x+2=0$, are

1. $x=\frac{-7\pm \sqrt{-17}}{8}$
2. $x=\frac{-4\pm \sqrt{17}}{8}$
3. $x=\frac{-7\pm \sqrt{17}}{8}$
4. $x=\frac{-7\pm \sqrt{11}}{8}$