# Roots of Quadratic Equation

## Trending Questions

**Q.**

If one zero of $2{x}^{2}-3x+k$ is reciprocal to the other, then find the value of $k$.

**Q.**

**Find the zeroes of the quadratic polynomial **$2{x}^{2}-9-3x$** and verify the relationship between zeroes and the coefficients.**

**Q.**

Find the zeroes of the quadratic polynomial $p\left(x\right)=ab{x}^{2}+({b}^{2}-ac)x-bc$ and verify the relationship between the zeroes and coefficients.

**Q.**Solve the following quadratic equation for x:

4x2+4bx−(a2−b2)=0

**Q.**Question 8

Show that 0.142857142857……=17

**Q.**

Find the zeroes of the polynomial ${x}^{2}+5x+6$ and verify the relationship between the zeroes and coefficients.

**Q.**The equation (Cosp−1)x2+(Cosp)x+Sinp=0, where x is a variable with real roots. then the interval of p may be any one of the following.

- (0, 2π)
- (−π, 0)
- (0, π)
- (−π2, π2)

**Q.**If two zeros of the polynomial f(x)=x3−4x2−3x+12 are √3 and −√3, then find its third zero. [2 MARKS]

**Q.**

Find the zeroes of the quadratic polynomial $2{x}^{2}-3+5x$ and verify the relationship between zeroes and the coefficients.

**Q.**In the question, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice.

Assertion(A) : x3 + x has only one real zero.

Reason(R) : A polynomial of nth degree must have 𝒏 real zeros.

- Both assertion (A) and reason (R) are true, but reason (R) is not the correct explanation of assertion (A).

- Both assertion (A) and reason (R) are true, and reason (R) is the correct explanation of assertion (A).
- Assertion (A) is false, but reason (R) is true.

- Assertion (A) is true, but reason (R) is false.

**Q.**

A fast train takes $3$ hours less than a slow train for a journey of $600\mathrm{km}$. If the speed of the slow train is $10\mathrm{km}/\mathrm{hr}$ less than that of the first train, find the speeds of the two trains.

**Q.**

The number of real solutions of the equation ${\left|x\right|}^{2}-3\left|x\right|+2=0$ is

$4$

$1$

$3$

$2$

**Q.**Question 10

One of the zeroes of the polynomial is 2x2+7x–4 is

A) 2

B) 12

C) −12

D) −2

**Q.**If one root of the quadratic equation 2x2+kx−6=0 is 2, find the value of k. Also, find the other root.

[2 MARKS]

**Q.**

Find the value of k, if x - 1 is a factor p(x) in each of the following cases:

(i) p(x)=x2+x+k

(ii) p(x)=2x2+kx+√2

(iii) p(x)=kx2−√2x+1

(iv) p(x)=kx2−3x+k

**Q.**

Find the zeroes of the quadratic polynomial $4{x}^{2}-4x-3$ and verify the relation between the zeroes and their coefficients.

**Q.**

Find the complex cube root of $8$.

**Q.**

Use Venn diagrams to verify De Morgan’s law of complementation (A∪B)’ = A’ ∩ B’

**Q.**

Factorise the following expression: $7x-42$

**Q.**34. What are the conditions for common root or roots of 2 Quadratic equations?

**Q.**Question 4

Does there exist a quadratic equation whose coefficients are rational but both of its roots are irrational? Justify your answer.

**Q.**

Louis want to carpet the rectangular floor of his basement.

The basement has an area of $864$ square feet.

The width of the basement is $\frac{2}{3}$ its length.

What is the length of Louiss basement $?$

**Q.**

Like surds are those surds which have same radicand but different order.

zero is a natural number

-1 is a whole number

**Q.**

The number of non-zero integral solutions of the equation ${\left|1-i\right|}^{x}={2}^{x}$ is

Infinite

$1$

$2$

None of these

**Q.**if the equations x^2+abx+c=0 and x^2+acx+b=0 have a common root the teir other roots satisfy the equati

**Q.**

Write the discriminant of $4{x}^{2}-20x+25=0$ and determine the nature of its root.

**Q.**

Let $a,b,c$ be real numbers, $a\ne 0$. If $\alpha $ is a root of ${a}^{2}{x}^{2}+bx+c=0$, $\beta $ is a root of ${a}^{2}{x}^{2}-bx-c=0$ and $0<\alpha <\beta $, then the equation ${a}^{2}{x}^{2}+2bx+2c=0$ has a root $\gamma $ that always satisfies.

$\gamma =\frac{[\alpha +\beta ]}{2}$

$\gamma =\left[\alpha \right]+\left[\frac{\beta}{2}\right]$

$\gamma =\left[\alpha \right]$

$\alpha <\gamma <\beta $

**Q.**In the question, a statement of assertion (A) is followed by a statement of reason (R). Mark the correct choice.

Assertion(A) : x3 + x has only one real zero.

Reason(R) : A polynomial of nth degree must have 𝒏 real zeros.

**Q.**

Find a quadratic polynomial, the sum and product of whose zeroes are $\frac{5}{6}$ and $\frac{1}{3}$ respectively.

**Q.**Question 37

The area of a semi-circle of radius 4r is

(a) 8πr2

(b) 4πr2

(c) 12πr2

(d) 2πr2