Answer :
The solutions to the quadratic equation 2x² = 4x – 7 is (2 + √10 i)/2 and (2 - √10 i)/2.
What is the root of the quadratic equation?
The values of variables satisfying the given quadratic equation are called their roots. In other words, x = α is a root of the quadratic equation f(x), if f(α) = 0. The real roots of equation f(x) = 0 are the x-coordinates of the points where the curve y = f(x) intersects the x-axis.
Let us use the quadratic formula to solve 2x² = 4x – 7.
Let's write the equation in its standard form.
2x² = 4x – 7
2x² - 4x + 7 = 0
a = 2, b = -4, c = 7, when we compare with the standard form of a quadratic expression ax² + bx + c = 0.
By quadratic formula,
x = [ -b ± √(b² - 4ac) ] / 2a
x = [ -(-4) ± √{(-4)² - 4(2)(7)} ] / 2(2)
x = [ 4 ± √{16 - 56} ] / 4
x = [ 4 ± √(-40) ] / 4
x = [ 4 ± 2√10 i ] / 4
x = (2 ± √10i)/2
values of x are : (2 + √10 i)/2 and (2 - √10 i)/2
Both the values of x are complex numbers.
Hence, the solutions to the quadratic equation 2x² = 4x – 7 is (2 + √10 i)/2 and (2 - √10 i)/2.
To learn more about the roots of the quadratic equation visit,
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