Find the roots of 2x^2-x+\frac{1}{8}=0 quadratic equations by factorization ?

byAmlesh Mahato •March 04, 2021

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Solution:

$Find the roots of 2x^2-x+\frac{1}{8}=0 quadratic equations by factorization ?$

⇨Multiply by 2 on both side

$\Rightarrow 4x^2-2x+\frac{1}{4}=0$

$\Rightarrow 4x^2-(1+1)x+\frac{1}{4}=0$

$\Rightarrow 4x^2-x-x+\frac{1}{4}=0$

$\Rightarrow 4x(x-\frac{1}{4})-1(x-\frac{1}{4})=0$

$\Rightarrow (4x-1)(x-\frac{1}{4})=0$

$\Rightarrow 4x-1=0,x-\frac{1}{4}=0$

$\Rightarrow x=\frac{1}{4},x=\frac{1}{4}$

Exercise 4.2

1. Find the roots of the following quadratic equations by factorisation:

(i) $x^2-3x-10=0$

(ii) $Find the roots of 2x^2+x-6=0 quadratic equations by factorization ?$

(iii) $Find the roots of \sqrt{2}x^2+7x+5\sqrt{2}=0 quadratic equations by factorization ?$

(iv) $Find the roots of 2x^2-x+\frac{1}{8}=0 quadratic equations by factorization ?$

(v) $\large 100x^{2}-20x+1=0$

3. Find two numbers whose sum is 27 and product is 182.

4. Find two consecutive positive integers, sum of whose squares is 365.

5. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

6. A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was ` 90, find the number of articles produced and the cost of each article.

Tags: Chapter-4 Exercise-4.2 Math- Class 10

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