Question
Solve the following quadratic equations by factorization:
$5x^2 - 3x - 2 = 0$
$5x^2 - 3x - 2 = 0$
✓
Answer
We have,$5x^2 - 3x - 2 = 0$
$\Rightarrow 5x^2 - 5x + 2x - 2 = 0$
$\Rightarrow 5x(x - 1) + 2(x - 1) = 0$
$\Rightarrow (x - 1)(5x + 2) = 0$
$\Rightarrow (x - 1) = 0$ or $5x + 2 = 0$
$\Rightarrow x = 1$ or $\text{x}=-\frac{2}{5}$
$\therefore$ x = 1 and $\text{x}=-\frac{2}{5}$ are the two roots of the given equation.
$\Rightarrow 5x^2 - 5x + 2x - 2 = 0$
$\Rightarrow 5x(x - 1) + 2(x - 1) = 0$
$\Rightarrow (x - 1)(5x + 2) = 0$
$\Rightarrow (x - 1) = 0$ or $5x + 2 = 0$
$\Rightarrow x = 1$ or $\text{x}=-\frac{2}{5}$
$\therefore$ x = 1 and $\text{x}=-\frac{2}{5}$ are the two roots of the given equation.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
A school has invited $42$ Mathematics teachers, $56$ Physics teachers and $70$ Chemistry teachers to attend a Science workshop. Find the minimum number of tables required, if the same number of teachers are to sit at a table and each table is occupied by teachers of the same subject.
→Find the area of triangle $\text{ABC}$ with $A (1,-4)$ and the mid$-$points of sides through $A$ being $(2,-1)$ and $(0,-1)$.
→The difference between two numbers is 26 and one number is three times the other. Find them.
Prove that $\sqrt{3}$ is an irrational number.
→The sum of $5^{\text {th }}$ and $9^{\text {th }}$ terms of an $A.P.$ is $72$ and the sum of $7^{th}$ and $12^{th}$ terms is $97$ .Find the $A.P.$
→Find the roots of the following quadratic equation (if they exist) by the method of completing the square.
$\sqrt{2}\text{x}^2-3\text{x}-2\sqrt{2}=0$
→$\sqrt{2}\text{x}^2-3\text{x}-2\sqrt{2}=0$
Find the solution of the pair of equations $\frac{\text{x}}{10}+\frac{\text{y}}{5}-1=0$ and $\frac{\text{x}}{8}+\frac{\text{y}}{6}=15$ Hence, find if $\text{y}=\lambda\text{x}+5$.
→Find the mean of each of the following frequency distributions:
→| Class interval | $0-8$ | $8-16$ | $16-24$ | $24-32$ | $32-40$ |
| Frequency | $6$ | $7$ | $10$ | $8$ | $9$ |
In the given figure, the sides $AB , BC$ and $CA$ of a triangle $ABC$ touch a circle with center $O$ and radius $r$ at $P , Q$ and R respectively. Prove that.
$a. AB + CQ = AC + BQ$
$b.$ area $(\Delta A B C)=\frac{1}{2}$ (perimeter of $\left.\Delta A B C\right) \times r$.
→$a. AB + CQ = AC + BQ$
$b.$ area $(\Delta A B C)=\frac{1}{2}$ (perimeter of $\left.\Delta A B C\right) \times r$.
Explain why 7 × 11 × 13 + 13 and 7 × 6 × 5 × 4 × 3 × 2 × 1 + 5 are composite numbers.