Question

# Find the roots of the following quadratic equations by factorisation:(i) $$\displaystyle { x }^{ 2 }-3x-10=0$$(ii) $$\displaystyle 2{ x }^{ 2 }+x-6=0$$(iii) $$\displaystyle \sqrt { 2 } { x }^{ 2 }+7x+5\sqrt { 2 } =0$$(iv) $$\displaystyle 2{ x }^{ 2 }-x+\frac { 1 }{ 8 } =0$$(v) $$\displaystyle 100{ x }^{ 2 }-20x+1=0$$

Solution

## i) $${ x }^{ 2 }-3x-10=0$$$$\Rightarrow { x }^{ 2 }-5x+2x-10=0$$$$\Rightarrow x(x-5)+2(x-5)=0$$$$\Rightarrow (x+2)(x-5)=0$$$$\Rightarrow x=5,-2$$ii) $${ 2x }^{ 2 }+x-6=0$$$$\Rightarrow { 2x }^{ 2 }+4x-3x-6=0$$$$\Rightarrow 2x(x+2)-3(x+2)=0$$$$\Rightarrow (x+2)(2x-3)=0$$$$\Rightarrow x=\dfrac{3}{2},-2$$iii) $${ \sqrt { 2 } x }^{ 2 }+7x+5\sqrt { 2 } =0$$$$\Rightarrow { \sqrt { 2 } x }^{ 2 }+2x+5x+5\sqrt { 2 } =0$$$$\Rightarrow \sqrt { 2 } x(x+\sqrt { 2 } )+5(x+\sqrt { 2 } )=0$$$$\Rightarrow (x+\sqrt { 2 } )(\sqrt { 2 } x+5)=0$$$$\Rightarrow x=-\sqrt { 2 } ,\dfrac{-5}{\sqrt { 2 }}$$iv) $${ 2x }^{ 2 }-x+\dfrac18=0$$$$\Rightarrow { 16x }^{ 2 }-8x+1=0$$$$\Rightarrow { 16x }^{ 2 }-4x-4x+1=0$$$$\Rightarrow 16x\left(x-\dfrac14\right)-4\left(x-\dfrac14\right)=0$$$$\Rightarrow \left(x-\dfrac14\right)(16x-4)=0$$$$\Rightarrow x=\dfrac{1}{4},\dfrac{1}{4}$$v) $${ 100x }^{ 2 }-20x+1=0$$$$\Rightarrow { 100x }^{ 2 }-10x-10x+1=0$$$$\Rightarrow { 10 }x(10x-1)-1(10x-1)=0$$$$\Rightarrow (10x-1)(10x-1)=0$$$$\Rightarrow x=\dfrac{1}{10},\dfrac{1}{10}$$MathematicsRS AgarwalStandard X

Suggest Corrections

0

Similar questions
View More

Same exercise questions
View More

People also searched for
View More