Formation of a Quadratic Equation From It's Roots

Q. Find the quadratic equation whose roots are the additive inverses of the roots of the equation $x^2-5x+6=0$

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

Q. Form a quadratic equation whose roots are -2, -3.

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

Q.

The roots of a quadratic equation are 5 and –2. The equation is -

1. $x^2–3x+10=0$

2. $x^2–3x–10=0$

3. $x^2+3x+10=0$

4. $x^2+3x–10=0$

Q.

The quadratic polynomial in x whose zeros are -a, 2a is:

1. (x – a) (x – a)

2. (x + a) (x – 2a)

3. (x + a) (x + 2a)

4. (x – 2a) (x + 2a)

Q. The quadratic equation which has D = 0 and a root as $\frac{1}{10}$ is

1. $x^2-20x-100=0$
2. $x^2-100x-100=0$
3. $100x^2-20x+1=0$
4. $100x^2-20x+100=0$

Q. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages was 48 years. Frame the equation for the above situation and predict the nature of its roots.

1. The roots are real and negative.
2. The roots are real and positive
3. The roots are real and equal
4. No real roots

Q. If one of the roots of a quadratic equation is 5 and its constant term is 165. Then the quadratic equation is :

1. $3x^2+33x+165=0$
2. $5x^2+25x+165=0$
3. $x^2+15x+165=0$
4. $x^2-38x+165=0$

Q. In the Maths test two students, while solving a quadratic equation, committed the following mistakes:
(i) One of them made a mistake in the constant term and got the roots as 5 and 9.
(ii) Another one committed an error in the coefficient of x and got the roots as 12 and 4.
But, in the meantime, they realised that they are wrong and they managed to get it right jointly. Find the correct quadratic equation.

1. $2x^2+7x-24=0$
2. $x^2-14x+48=0$
3. $3x^2-17x+52=0$
4. $x^2-44x+14=0$

Q.

The quadratic polynomial in x whose zeros are -a, 2a is:

1. (x – a) (x – a)

2. (x + a) (x – 2a)

3. (x + a) (x + 2a)

4. (x – 2a) (x + 2a)

Q. If the square of twice a number is 9 more than thrice the square of the given number, then the number can be .

1. 3 or -3
2. 4 or -4
3. 5 or -5
4. 6 or -6