the factorisation of 6x ^2+11+3 is
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SOLUTION :
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Quadratic equation is generally written in the form of aX^2 + bX + c, where X is variable with maximum degree of two and a, b and c are numeric coefficient. Numeric coefficients are helpful in solving quadratic equation.
In the equation 6X^2 + 11X + 3,
a is 6, b is 11 and c is 3
To factor this equation, using decomposition method, a is multiplied with c and then factored in such a way that sum of both the factors must be equal to b. In the above equation
a × c = 18, if we factorize 18, we get (1×2×3×3)
(1)×(2×3×3) = 1 × 18, 18 + 1 = 19….doesn't match
(1×3)×(2×3) = 3 × 6 = 18, 3 + 6 = 9…doesn't match
(1×2)×(3×3) = 2 × 9 = 18, 9 + 2 = 11…right match
So this way we have found out that 2×9 or 9×2 is the right match for b.
Now keep coefficient a and variable X in mind which is 6X. In two brackets add 6X with both the factors and multiply them.
(6X + 9)×(6X + 2) = 0, In both this brackets, we can see that first bracket is divisible by 3 and second bracket is divisible by 2, so
(2X + 3)×(3X + 1) = 0…we have now reached the final step which will give us two solutions for X.
2X + 3 = 0 and 3X + 1 = 0
2X = - 3, X = -3/2, 3X = -1, X = -1/3