Solving Using Quadratic Formula When D>0

Q.

Find the zeros of the polynomial $x^2-3x-m(m+3).$

Q.

The zeros of the polynomial $x^2-\sqrt{2}x-12$ are

1. (b) $3\sqrt{2},-2\sqrt{2}$

2. (c) $3-\sqrt{2},2\sqrt{2}$

3. (a) $\sqrt{2},-\sqrt{2}$

4. (d) $3\sqrt{2},2\sqrt{2}$

Q.

The zeros of the polynomial $4x^2+5\sqrt{2}x-3$ are

1. (c)$\frac{-3\sqrt{2}}{2},\frac{\sqrt{2}}{4}$

2. (a) $-3\sqrt{2},\sqrt{2}$

3. (b) $-3\sqrt{2},\frac{\sqrt{2}}{2}$

4. (d) none of the these

Q.

Solve the following equation:

$\frac{2x}{x-3}+\frac{1}{2x+3}+\frac{3x+9}{(x-3)(2x+3)}=0;x\ne 3,x\ne -\frac{3}{2}$

Q.

Find the roots of the quadratic equation, 3x² – 5x + 2 = 0, using quadratic formula.

1. $\frac{(5\pm 2)}{6}$

2. $\frac{(5\pm 1)}{6}$

3. $\frac{(4\pm 1)}{6}$

4. $\frac{(7\pm 1)}{6}$

Q.

If X = 5 + 2$\sqrt{6}$ Find the value of X + $\frac{1}{X}$

1. $20$

2. $10\sqrt{2}$

3. $15\sqrt{2}$

4. $10$

Q.

If the zeroes of the quadratic polynomial ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}$, where $\mathrm{c}\ne 0$, are equal, then

1. $\mathrm{c}$ and $\mathrm{a}$ have opposite sign

2. $\mathrm{c}$ and $\mathrm{b}$ have opposite sign

3. $\mathrm{c}$ and $\mathrm{a}$ have the same sign

4. $\mathrm{c}$ and $\mathrm{b}$ have the same sign

Q.

A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/hr more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed?

Q.

A train travels a distance of $480km$ at a uniform speed. If the speed had been $8km/h$ less, then it would have taken $3hours$ more to cover the same distance. Find the speed of the train.

Q.

A train covers a distance of 480 km at a uniform speed. If speed had been 8km /hr less then it would have taken 3 hours more to cover the same distance. Find the usual speed of the train.

Q. A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed.If the truck covers the total distance in 5 hours, find the first speed of the truck.

Q.

Verify whether the following are zeroes of the polynomial, indicated against them: $\mathrm{p}\left(\mathrm{x}\right)=3\mathrm{x}+1,\mathrm{x}=\frac{-1}{3}$

Q.

The area of a square park is the same as of a rectangular park. If the side of the square park is 60 m and the length of the rectangular park is 90 cm, find the breadth of the rectangular park

Q.

Solve the quadratic equation $x^2-3x-9=0$ for x and give your answer correct to two decimal places.

Q.

Three consecutive positive integers are such that the sum of the square of the first and the product of the other two is 46. Find the integers.

Q.

If the price of a book is reduced by Rs.5, a person can buy 4 more books for Rs.600. Find the original price of the book.

Q.

Find the roots of quadratic equation x² - 4x + 4 = 0 using the quadratic formula.

1. 4, -2

2. 2, 2

3. -2, -2

4. 2, 3

Q.

Question 84

Solve the following:

The sum of three consecutive even natural numbers is 48. Find the greatest of these numbers.

Q.

Find the zeroes of the polynomial $x^2+4\sqrt{3}x-15=0$ by factorization method.

Q.

Using the quadratic formula, solve for $x$:

$16x^2-8a^{2}x+(a^4-b^4)=0$

Q.

Solve each of the following quadratic equations:
$\left(\frac{4x-3}{2x+1}\right)-10\left(\frac{2x+1}{4x-3}\right)=3,x\ne \frac{-1}{2},\frac{3}{4}$

Q.

Solve $x^2-7x+12=0$ by Formula Method.

Q.

Find the three consecutive numbers such that the sum of their square will be $434$.

Q. Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:
(i) $2x^2-3x+5=0$
(ii) $3x^2-4\sqrt{3}x+4=0$
(iii) $2x^2-6x+3=0$

Q.

Using the quadratic formula, solve for $x$:

$9x^2-6ax+a^2-b^2=0$

Q.

Solve the quadratic equation $x^2-3(x+3)=0$; Give your answer correct to two significant figures.

Q. By increasing the list price of a book by ₹12, a person can buy 24 books less for ₹1728. The original price of the book was_____.

1. ₹20
2. ₹24
3. ₹16
4. ₹18

Q. What are zeros of polynomial ?

Q.

The zeros of the polynomial $x^2-2x-3$are

1. (b) -3, -1

2. (a) -3, 1

3. (c) 3, -1

4. (d) 3, 1

Q.

Solve the Quadratic equation $m^2$-14m+13=0 by factorization. ( 1 mark)