Answer:
Solve 0 = 4x2 + 12x + 9. select the equation that shows the correct substitution of a, b, and c in the quadratic formula.
We know that quadratic equation for:
ax^2 + bx + c= 0…………(1) is
X = {- b + - √( b^2 -4ac) } / 2a ……….(2)
for calculating the value of x. where a, b and c values are given in numeric.
So , here if we compare the value of 0 = 4x^2 + 12x + 9 with equation no 1 then we can get
a = 4 , b= 12 and c = 9
So from these we can get
X = {- 12 + - √(12^2 – 4*4*9)} / 2*4
X = {- 12 + - √(12*12 – 4*4*9) } / 2*4
X = - 12 + - (√144 – 144) / 2*4
X = - 12 + 0 /8
X= - 3/2
So the implemented equation of 0 = 4x^2 + 12x + 9. Will be X ={ - 12 + - √(12*12 – 4*4*9 )/ 2*4} and the calculated value of x will be -3/2
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We get the value of x as - 3 / 2 and the quadratic equation is represented by a x² + b x + c= 0.
We know that the formula for quadratic equation is given by:
a x² + b x + c= 0
Here, we have the quadratic equation as:
4x² + 12 x + 9 = 0
We will solve it by using middle term splitting.
We can write the equation as:
4 x² + 6 x + 6 x + 9 = 0
Taking common factors:
2 x ( 2 x + 3) + 3 ( 2 x + 3) = 0
Again taking the common factors:
(2 x + 3)(2 x + 3) = 0
Solving it to get the value of x:
x = - 3 / 2 and - 3 / 2.
Therefore, we get the value of x as - 3 / 2 and the quadratic equation is represented by a x² + b x + c= 0.
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