Question

solve the following equation by factorization-) 15x²-28=x​

Answer 1

Given:-

p(x)=0

→15x²-x-28=0

To find:-

The Value of x?

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$\pink{\boxed{\red{\underline{\orange{\mathrm{Proof:-}}}}}}$

→15x²-x-28=0

S=-1[Sum of Equations]

P=-420[Product of Equations]

★As their is no Common factor giving us Sum as 1 and Product as 420 we can use another method★

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•USING Discriminant Formula:-

d=b²-4ac

a=15

b=-1

c=-28

★Putting the Values★

→d=(-1)²-4×15×-28

→d=1+1680

→d=1681

→√d=±√1681

→√d=±41

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Taking x(+)→$\frac{-b+ \sqrt{d}}{2a}$

x→$\frac{-(-1)+41}{2×15}$

x→$\frac{\cancel{42}}{\cancel{30}}$

x→$\frac{7}{5}$

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Taking x(-)→$\frac{-b- \sqrt{d}}{2a}$

x→$\frac{-(-1)-41}{2×15}$

x→$\frac{\cancel{40}}{\cancel{30}}$

x→$\frac{4}{3}$

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Answer 2

$\bf{15 {x}^{2} - 28 = x } \\ \\ \rightarrow \: \sf{15 {x}^{2} - x - 28 = 0 } \\ \\ \sf{by \: middle \: term \: splitting \: method } \\ \\ \rightarrow \: \sf{15 {x}^{2} - (21 - 20)x - 28 = 0} \\ \\ \rightarrow \: \sf{15 {x}^{2} - 21x + 20x - 28 = 0 } \\ \\ \rightarrow \: \sf{3x \big(5x - 7 \big) + 4 \big(5x - 7 \big) = 0} \\ \\ \rightarrow \: \sf{ \big(5x - 7 \big) \big(3x + 4 \big) = 0}$

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$\bf{5x - 7 = 0} \\ \\ \rightarrow \: \fbox{ \sf{x = \frac{7}{5} }}$

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$\bf{3x + 4 = 0} \\ \\ \rightarrow \: \fbox{ \sf{x = \dfrac{ - 4}{3} }}$

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$\bf{x = \dfrac{7}{5} , \: \dfrac{ - 4}{3} }$