Math, asked by RITESHprajapati, 11 months ago

solve the equation
2x { }^{2}  + 13x + 15 = 0
by factorisation method,by completing the square method and by using the formula method.verify that you will get the same roots every time.​

Answers

Answered by bedabrata85
9

Mate here is your answer please mark braineliest

FACTORIZATION METHOD

2 {x}^{2}  + 13x + 15 = 0 \\  =  > 2 {x}^{2}  + 10x + 3x + 15 = 0 \\  =  > 2x(x + 5) + 3(x + 5) = 0 \\  =  > (2x + 3)(x + 5) = 0 \\  =  > x =   - \frac{3}{2} or \: x =  - 5

COMPLETING SQUARE METHOD

 {2x}^{2}  + 13x + 15 = 0 \\    =  > \frac{2 {x}^{2} }{2}  +  \frac{13}{2} x +  \frac{15}{2}  =  \frac{0}{2}  \\   =  >  {x}^{2}  +  \frac{13}{2} x =  -  \frac{15}{2}  \\  =  >  {x}^{2}  + 2 \times  \frac{13}{4}  \times x +  (\frac{13}{4}) ^{2}   =  -  \frac{15}{2}  + ( \frac{13}{4} ) ^{2}  \\  =  >  {(x +  \frac{13}{4}) }^{2}  =    - \frac{15}{2}  +  \frac{169}{16}  \\  =  >  {(x +  \frac{13}{4}) }^{2}  =  \frac{ - 120 + 169}{16}  \\  =  > x +  \frac{13}{4}  =   \frac{ + }{}  \sqrt{ \frac{49}{16} }  \\  =  > x =  \frac{7}{4}  -  \frac{13}{4} or \:   - \frac{7}{4}  -  \frac{13}{4}  \\  =  > x =   - \frac{6}{4}  =  -  \frac{3}{2}  \:  \: or \:  \:  -  \frac{20}{4} =  - 5

FORMULA METHOD

HERE , a= 2 , b= 13 , c= 15

d =  {b}^{2}  - 4ac \\  =  > d =  {13}^{2}  - 4 \times 2 \times 15 \\  =  > d = 169 - 120 \\  =  > d = 49 \\   =  >  \sqrt{d}  = 7

So, By quadratic formula,

x =  \frac{ - b \frac{ + }{}  \sqrt{d} }{2a}  \\  =  > x =  \frac{ - 13 + 7}{2 \times 2}  \: or \:  \frac{ - 13 - 7}{2 \times 2}  \\  =  > x =  \frac{ - 6}{2 \times 2} =  -  \frac{3}{2}   \: or \:  \frac{ - 20}{2 \times 2}  =  - 5

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