Solving a Quadratic Equation by Factorization Method

Q.

Factorize the equation: $x^3-3x^2-9x-5$.

Q.

Write the zeros of the quadratic polynomial $f\left(x\right)=4\sqrt{3}{x}^2+5x-2\sqrt{3}$.

Q.

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

Q.

Solve each of the following quadratic equations:
$x^2+2\sqrt{2}x-6=0$

Q.

A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed. If it takes 3 hours to complete total journey, what is its original average speed?

Q.

Solve the following quadratic equation by factorization.
$3x^2-2\sqrt{6x}+2=0$

Q.

Write the zeros of the polynomial $x^2-x-6$.

Q.

√2x+√3y=0, √3x-√8y=0 solve by elimination method

Q.

Solve each of the following quadratic equations:
$\frac{a}{(x-b)}+\frac{b}{(x-a)}=2,x\ne b,a$

Q.

The product of two consecutive positive integers is 306. Find the integers.

Q. The sum of the squares of two consecutive odd numbers is 394. Find the numbers.

Q. Three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two by 60.
Find the numbers.

Q.

A train travels 360 km at a uniform speed. If the speed had been 5 km /hr more, it would have taken 1 hour less for the same journey. Form the quadratic equation to find the speed of the train.

Q.

The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages (in years) was 124. Determine their present ages.

Q.

Solve each of the following quadratic equations:
(i) $\frac{1}{x-1}-\frac{1}{x+5}=\frac{6}{7},x\ne 1,-5$
(ii) $\frac{1}{2x-3}-\frac{1}{x-5}=1\frac{1}{9},x\ne \frac{3}{2},5$

Q.

Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” (Isn’t this interesting?) Represent this situation algebraically and graphically.

Q.

Find HCF of 81 and 237 and express it as a linear combination of 81 and 237 i.e., HCF (81, 237)= 81x + 237y for some x and y. Please explain.

Q.

The sum of two natural numbers is 9 and the sum of their reciprocal is $\frac{1}{2}$. Find the numbers.

Q.

A train, travelling at a uniform speed for $360km$, would have taken $48$ minutes less to travel the same distance if its speed were $5km/hr$ more. Find the original speed of the train.

Q.

Solve the following quadratic equation by factorization.
$\frac{3}{x+1}-\frac{1}{2}=\frac{2}{3x-1},x\ne -1,\frac{1}{3}$

Q.

Solve the following quadratic equation by factorization.
$\frac{x-a}{x-b}+\frac{x-b}{x-a}=\frac{a}{b}+\frac{b}{a}$

Q. Question 11
Sum of the areas of two squares is 468$m^2$. If the difference of their perimeters is 24 m, find the sides of the two squares.

Q. Question 4
If $\frac{1}{2}$ is a root of equation $x^2+kx-\frac{5}{4}=0$, then the value of k is
(A) 2
(B) – 2
(C) 1/4
(D) 1/2

Q.

Prove that$\frac{cosA-sinA+1}{cosA+sinA-1}=cosecA+cotA$

Q.

Solve the following quadratic equation by factorization.
$a(x^2+1)-x(a^2+1)=0$

Q. In an exam one Mark is awarded for one correct answers and 1\4 Marks is deducted for each wrong answers. A student who awarded a total of 120 questions, got 90 Mark. How many questions did he answer correctly

Q.

the difference of the square of two number is 180 the square of the smaller number is 8 times the larger number find the two numbers

Q.

The numerator of a fraction is 3 less than the denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction is $\frac{29}{20}$. Find the original fraction.

Q.

Some students planned a picnic. The total budget for food was Rs.2000. But, 5 students failed to attend the picnic and thus the cost for food for each member increased by Rs.20. How many students attended the picnic and how much did each student pay for the food?

Q.

The difference of two natural numbers is 3 and the difference of their reciprocals is $\frac{3}{28}$