
The equation where has no real roots if
A.
B.
C.
D.None of these
Answer
500.4k+ views
Hint: Given equation is of the form . This is a quadratic equation. The nature of the roots of a quadratic equation depends on the term . So let’s check it with the given equation.
Complete step-by-step answer:
Now the given equation is . Comparing this with the general quadratic equation we get a=1, b=-p and c=q. Also it is given that .
The term that decides the nature of the roots of the equation is,
Now if then the given equation has no real roots because, roots of the equation is given by,
Now if the term in the square root is negative or less than zero then the roots so obtained are imaginary. Thus the equation has no real roots then.
Note: We will also have a look on other conditions of the nature of the roots .
Complete step-by-step answer:
Now the given equation is
The term that decides the nature of the roots of the equation is,
Now if
Now if the term in the square root is negative or less than zero then the roots so obtained are imaginary. Thus the equation has no real roots then.
Note: We will also have a look on other conditions of the nature of the roots .
If | The roots are real and unequal. |
If | The roots are real and equal. |
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