$4x^2 + 4x - 3 = 0$
$-\frac{3}{2}, \frac{1}{2}$
Solving the Quadratic Equation $4x^2 + 4x - 3 = 0$
To find the roots of the quadratic equation $4x^2 + 4x - 3 = 0$, we can use the factorization method.
Factorization Steps
- Identify Coefficients: The equation is in the form $ax^2 + bx + c = 0$, where $a=4$, $b=4$, and $c=-3$.
- Find Product and Sum: We need two numbers that multiply to $a \times c = 4 \times (-3) = -12$ and add up to $b = 4$. These numbers are $6$ and $-2$.
- Rewrite Middle Term: Rewrite the equation by splitting the middle term ($4x$) using these numbers:
$4x^2 + 6x - 2x - 3 = 0$
- Factor by Grouping: Group the terms and factor out common factors:
$2x(2x + 3) - 1(2x + 3) = 0$
- Factor Common Binomial: Factor out the common binomial $(2x + 3)$:
$(2x - 1)(2x + 3) = 0$
- Solve for x: Set each factor equal to zero and solve for $x$:
- $2x - 1 = 0 \implies 2x = 1 \implies x = \frac{1}{2}$
- $2x + 3 = 0 \implies 2x = -3 \implies x = -\frac{3}{2}$
Conclusion
The roots of the equation $4x^2 + 4x - 3 = 0$ are $x = \frac{1}{2}$ and $x = -\frac{3}{2}$.
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Important Questions from Quadratic Equations
If the graph of a quadratic polynomial lies entirely above x-axis, then which one of the following is correct?
If the roots of the equation x 2+ px + q = 0 are tan 19° and tan 26°, then which one of the following is correct?
If x 2- px + 4 > 0 for all real values of x, then which one of the following is correct?
If 2 + i is a root of the equation x 2- ax + 1 = 0, then the value of a is:
If \(\tan \left( {\frac{α }{2}} \right)\) and \(\tan \left( {\frac{β }{2}} \right)\) are the roots of the equation 8x 2- 26x + 15 = 0, then the value of cos (α + β) will be
