Formulation of Quadratic Equation

Q.

How do I check for extraneous solutions?

Q.

What is the relationship between the degree of a polynomial and the maximum number of zeros it can have?

Q. Find the quadratic equation whose roots are $\frac{6+\sqrt{3}}{3}\text{and}\frac{6-\sqrt{3}}{3}.$

1. $x^2-16x+9=0$
2. $3x^2-12x+11=0$
3. $6x^2-4x+1=0$
4. $7x^2-4x+11=0$

Q.

A quadratic equation whose roots are $2+\frac{1}{\sqrt{2}}$ and $2-\frac{1}{\sqrt{2}}$ is:

1. $x^2-7x+8$ = 0

2. $2x^2-8x+7$ = 0

3. $2x^2-7x+8$ = 0

4. $x^2-8x+7$ = 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. Find the sum of zeros of the polynomial $2x^2-9$

1. $0$
2. $1$
3. $-1$
4. $2$

Q. If 1 is one of the zeroes of the polynomial $x^2-x+k$, then the value of k is _________.

1. -2
2. 0
3. 2
4. 4

Q. The zeroes of the polynomial $x^2-3x-m(m+3)$ are:

Q. The height of a triangle is 3 m more than its base. If the area of the triangle is 35 sq.m. , then find its height.

1. $10m$
2. $7m$
3. $14m$
4. $5m$

Q. If the speed of a train is reduced by 40 km/hr, it takes 20 minutes more to cover 1200 km. Find the speed of the train.

1. 400 km/hr
2. 360 km/hr
3. 420 km/hr
4. 380 km/hr

Q.

A takes 6 days less than the time taken by B to finish a piece of work. If both A and B together can finish it in 4 days, find the time taken by B alone to finish the work.

1. B alone can finish the work in 9 days

2. B alone can finish the work in 8 days

3. B alone can finish the work in 12 days

4. B alone can finish the work in 5 days

Q.

Find the numbers such that the square of number is 15 lesser than twice the number.

1. 8

2. 9

3. -3

4. 5

Q.

A quadratic equation whose roots are $2+\frac{1}{\sqrt{2}}$ and $2-\frac{1}{\sqrt{2}}$ is:

1. $x^2-7x+8$ = 0

2. $2x^2-8x+7$ = 0

3. $2x^2-7x+8$ = 0

4. $x^2-8x+7$ = 0

Q.

A natural number, when decreased by 13, equals 140 times its reciprocal. Find the number.

1. x = 20

2. x = 90

3. x = 10

4. x = 60

Q.

How do you find the polynomial function with leading coefficient $2$ that has the given degree and zeroes: degree $3$:zeroes $-2,1,4?$

Q. Zeroes of quadratic polynomials are given on the left. Match them with the respective quadratic polynomials.

1. $x^2-2x-24$
2. $x^2-10x+25$
3. $64x^2-1$
4. $x^2+x-30$

Q.

One leg of a right angled triangle exceeds the other leg by 4 inches. The hypotenuse is 20 inches. Find the length of the shorter leg of the triangle.

1. 12 inches

2. 7 inches

3. 20 inches

4. 14 inches

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. One of the roots of a quadratic equation that has integral coefficients is $\frac{-4}{5}+\frac{3\sqrt{2}}{8}i$. Which of the following describes the quadratic equation?

1. $800x^2+1280x+737=0$
2. $800x^2+1280x-287=0$
3. $800x^2+1280x+287=0$
4. $800x^2-1280x+737=0$
5. $800x^2-1280x+287=0$

Q.

A takes 6 days less than the time taken by B to finish a piece of work. If both A and B together can finish it in 4 days, find the time taken by B alone to finish the work.