Factorize -3 x 2-5 x -2 -3-0 into ax - b cx - d -0- What is the value of a - b - c - d -

Multiply √(3) with 2√(3) and we get 6 Pairs of 6 are 1×6 = 6 sum 1+ 6 = 7 2×3= 6 sum 2+ 3 = 5 So our required pair is 2 and 3 ⇒ √(3) x^2 + 5x ...

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Standard X

Mathematics

Solving a Quadratic Equation by Splitting the Middle Term

Factorize √3 ...

Question

Factorize $\sqrt{3}$ $x^{2}$ + 5x + 2 $\sqrt{3}$ = 0 into (ax+b)(cx+d)=0. What is the value of a + b + c - d ?

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Solution

Multiply $\sqrt{3}$ with 2 $\sqrt{3}$ and we get 6

Pairs of 6 are

1 $\times$ 6 = 6 sum 1+ 6 = 7

2 $\times$ 3= 6 sum 2+ 3 = 5

So our required pair is 2 and 3

$\Rightarrow$ $\sqrt{3}$ $x^{2}$ + 5x + 2 $\sqrt{3}$ = 0

$\Rightarrow$ $\sqrt{3}$ $x^{2}$ + 3x + 2x +2 $\sqrt{3}$ = 0

$\Rightarrow$ $\sqrt{3}$ x(x+ $\sqrt{3}$ )+ 2(x+ $\sqrt{3}$ )= 0

$\Rightarrow$ ( $\sqrt{3}$ x + 2) (x + $\sqrt{3}$ ) = 0

a= $\sqrt{3}$ , b = 2, c = 1, d = - $\sqrt{3}$

a + b + c - d = 3

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Factorize √3 x2 + 5x + 2√3 = 0 into (ax+b)(cx+d)=0. What is the value of a + b + c - d ?

Factorize $\sqrt{3}$ $x^{2}$ + 5x + 2 $\sqrt{3}$ = 0 into (ax+b)(cx+d)=0. What is the value of a + b + c - d ?