Question

EXERCISE 4.2
1. Find the roots of the following quadratic equations by factorisation:
(i) x2 – 3x - 10 = 0
​

Answer 1

Answer:

here's your answer......

Answer 2

S O L U T I O N :

We have quadratic equation p(x) = x² - 3x - 10 = 0.

$\underline{\underline{\tt{Using\:\:by\:\:prime\:\:factorisation\:\:method\::}}}$

→ x² - 3x - 10 = 0

→ x² -5x + 2x - 10 = 0

→ x(x - 5) + 2(x - 5) = 0

→ (x - 5) (x + 2) = 0

→ x - 5 = 0  Or  x + 2 = 0

→ x = 5  Or  x = -2

Thus,

The roots of the quadratic equation will be 5 & -2 .

We can use another method like by quadratic formula;

$\boxed{\bf{x = \frac{-b\pm\sqrt{b^{2} - 4ac} }{2a} }}$

As we know that given quadratic compared with ax² + bx + c;

• a = 1
• b = -3
• c = -10

Now,

$\mapsto\tt{x = \dfrac{-b\pm \sqrt{b^{2} - 4ac} }{2a}}$

$\mapsto\tt{x = \dfrac{-(-3)\pm \sqrt{(-3)^{2} - 4\times 1 \times (-10)} }{2\times 1}}$

$\mapsto\tt{x = \dfrac{3\pm \sqrt{9+40} }{2}}$

$\mapsto\tt{x = \dfrac{3\pm \sqrt{49} }{2}}$

$\mapsto\tt{x = \dfrac{3\pm 7 }{2}}$

$\mapsto\tt{x = \dfrac{3 + 7 }{2} \:\:\:Or\:\:\:x = \dfrac{3-7}{2} }$

$\mapsto\tt{x = \cancel{\dfrac{10}{2}} \:\:\:Or\:\:\:x = \cancel{\dfrac{-4}{2} }}$

$\mapsto\bf{x = 5 \:\:\:Or\:\:\:x = -2}$

So, It's root of the given quadratic equation .