Question

solve by factorization method​

Answer 1

$\underline{\underline{\textsf{\maltese\:\: Question :}}}$

Solve by factorisation method.

3x² + 10 = 11x

$\underline{\underline{\textsf{\maltese\:\: Solution :}}}$

3x² + 10 = 11x

⇒ 3x² + 10 - 11x = 0

⇒ 3x² - 11x + 10 = 0

⇒ 3x² - 6x - 5x + 10 = 0

⇒ 3x(x - 2) -5(x - 2) = 0

⇒ (3x - 5) (x - 2) = 0

$\pink\bigstar \;\bf{Now \; finding \; the \; roots \; or \; zeros.}$

✎ $\underline{\bf{CASE \; \; I}}$

3x - 5 = 0

⇒ 3x = 5

⇒ x = $\bf \dfrac{5}{3}$

✎ $\underline{\bf{CASE \; \; II}}$

x - 2 = 0

⇒ x = 2

${ \pink{\boxed{ \red{\bf{\therefore \; \; x = \dfrac{5}{3} \; \; OR\; \; 2 }}}}}$

Answer 2

$\huge\sf\underline\red{Solution}$

3x² + 10 = 11x

So, Transpose 11x to LHS

3x²+10-11x = 0

3x²-11x+10 = 0

Now split the middle term

10×3 =30

1×30=30

2×15=30

3×10=30

5×6=30

10×3=30

Sum sholud be - 11. So, -5x-6x = -11x

______________________________

Now splitting,....

3x²-5x-6x+10 = 0

3x²-6x-5x+10 =0

3x(x-2)-5(x-2)=0

(x-2)(3x-5)=0

x-2 =0

x=2

_______

3x-5=0

3x=5

x=5/3

_______

So values of x are 2,5/3

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