if a quadratic equation with real coefficents has a discriminant of 10, then what type of roots does it have?
A-2 real, rational roots
B-2 real, irrational roots
C-1 real, irrational roots
D-2 imaginary roots
Hints: here are the possible situations:
When discriminant is negative:
2 imaginary roots
When discriminant is a positive perfect square, such as 1, 4, 9, 16... and all coefficients are rational:
2 real, rational roots
When discriminant is zero, and either coefficient a or b is irrational:
1 real, irrational roots
When discriminant is a positive number but not a perfect square:
2 real, irrational roots
To determine the type of roots a quadratic equation with real coefficients has, we need to examine the discriminant. The discriminant is found by taking the square root of the expression b^2 - 4ac, where 'a', 'b', and 'c' are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
In this case, the discriminant is 10. Since the discriminant is positive, we can conclude that there are two real roots.
Now, let's determine whether the roots are rational or irrational. To do this, we need to consider if the discriminant is a perfect square or not.
Since the square root of 10 is an irrational number, the discriminant is not a perfect square. Therefore, the roots of the quadratic equation will be irrational.
In conclusion, the quadratic equation with a discriminant of 10 will have 2 real, irrational roots. Therefore, the correct answer is B- 2 real, irrational roots.
To determine the type of roots of a quadratic equation, we look at the discriminant.
The discriminant is calculated using the formula: D = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation (in the form ax^2 + bx + c = 0).
In this case, the discriminant is given as 10.
If the discriminant is positive, it means that there are two real roots.
If the discriminant is zero, it means that there is one real root.
If the discriminant is negative, it means that there are two imaginary roots.
Since the discriminant is positive (10), the quadratic equation will have two real roots.
Therefore, the correct answer is A- 2 real, rational roots.