Question

After Solving the following quadratic equation by factorization, the roots are(approx nearest whole no) to 6.

(x - 5)(x - 6) = $\frac{25}{(24{)}^2}$

• A. True
• B. False

Answer 1

The correct option is A True

Given,

$(x-6)(x-5)=\frac{25}{(24{)}^2}$

Let,

$x-6=a$

$\Rightarrow x-5=a+1$

$\Rightarrow a(a+1)=\frac{24+1}{(24{)}^2}=\frac{1}{24}(1+\frac{1}{24})$

$\Rightarrow a^2+(1+\frac{1}{24})a-\frac{a}{24}-\frac{1}{24}(1+\frac{1}{24})=0$

$\Rightarrow a(a+1+\frac{1}{24})-\frac{1}{24}(a+1+\frac{1}{24})=0$

$(a+1+\frac{1}{24})(a-\frac{1}{24})=0$

$\Rightarrow (a+\frac{25}{24})(a-\frac{1}{24})=0$

$\therefore a=-\frac{25}{24},\frac{1}{24}$

when, $a=-\frac{25}{24}$

$x=a+6=4\frac{23}{24}$

when, $a=\frac{1}{24}$

$x=a+6=6\frac{1}{24}$