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The quadratic equation has two real solutions because the value of D is positive and greater than zero or D > 0 option (B) is correct.
Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
As we know, the formula for the roots of the quadratic equation is given by:
[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]
We have a quadratic equation:
y = x² - 11x + 7
As we know, the discriminant formula is used to find the nature of the roots.
The discriminant formula is:
D = b² - 4ac
The standard quadratic equation is:
y = ax² + bx + c
a = 1, b = -11, and c = 7
Plug the values in the formula:
D = (-11)² - 4(1)(7)
D = 121 - 28
D = 93
As the D is positive and greater than zero or D > 0
Thus, the quadratic equation has two real solutions because the value of D is positive and greater than zero or D > 0 option (B) is correct.
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