find the nature of root of the equation 2x^2-6x+7
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EXPLANATION.
Quadratic equation.
⇒ 2x² - 6x + 7 = 0.
As we know that,
D = Discriminant Or b² - 4ac.
⇒ D = (-6)² - 4(2)(7).
⇒ D = 36 - 56.
⇒ D = -20.
⇒ D < 0 Roots are imaginary.
MORE INFORMATION.
Maximum & minimum value of quadratic equation.
In a quadratic expression ax² + bx + c.
(1) = If a > 0, quadratic expression has least value at x = -b/2a. This least value is given by = 4ac - b²/4a = -D/2a.
(2) = If a < 0, quadratic expression has greatest value at x = -b/2a. This greatest value is given by = 4ac - b²/4a = -D/2a
Given Quadratic equation is
To find the nature of roots, we have to find Discriminant.
We know,
Now,
Three cases arises.
So,
For the given Quadratic equation
So, it implies, Quadratic equation has no real roots.