solve the equation:3x^2 +5x -12 = 0 using the formula.
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Given the equation:
3x^2 + 5x -12 = 0
We need to solve for x.
We will use the formula to find the roots of the quadratic equations.
We know that:
x = [ -b +- sqrt(b^2-4ac)/ 2a
==> x1= ( -5 + sqrt(25-4*3*-12)]/2*3
= (-5 + sqrt(169) / 6
= (-5 +13)/6 = 8/6 = 4/3
==> x1= 4/3
==> x2= (-5 -13)/6 = -18/6 = -3
==> x2= -3
Then the solution for the quadratic equation is:
x= { 4/3 , -3}
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3x^2 +5x -12 = 0
There is another way for solving quadratic equations i.e factorization
3x^2 +5x -12 = 0 can be factored as
for this we will be splitting the 5x in a way that the product of the parts is equal to the product of 3 and -12
3x^2+9x-4x-12=0
3x(x+3)-4(x+3)=0
(x+3)(3x-4)=0
so x=-3,4/3
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