1.Which is the value of b²-4ac in the quadratic equation x²+5x+4=0?
A.-9 B.9 C.-41 D.41
2.Which are the solutions of 4t²-9=0?
A.one real solution B.two real solution C.no real solution D two irrational solution
3.What is the nature of the roots of the quadratic equation 2x²+3x-14=0?
A.the roots are not equal
B.the roots are irrational and are not equal.
C.the roots are rational and are equal.
D.the roots are rational and are not equal.
4.What are the roots if k>0 in the form x²=√k?
A.no real root
B.two real roots
C one real root
D.negative root
5.Which are the roots of the quadratic equation of x²-10x=-9?
A.-1 and -9
B.1 and 9
C.7 and 3
D.7 and -3
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Verified answer
1. using the formula: b²-4ac
where: a = 1 , b = 5 , and c = 4
» hence , the correct answer is B (9)
2. Using the discriminant formula: b²-4ac
Given: 4t²-9=0 , where a= 4 , b = 0 , c = -9
If the discriminant is greater than zero and is a perfect square. The nature of the roots are real , rational , and are equal. This implies it has 2 real solutions.
» Hence , the correct answer is B(two real solution)
3. Using the discriminant formula: b²-4ac
Given: 2x²+3x-14 = 0 , where a = 2 , b = 3 , and c = -14
If the discriminant is greater than zero and not a perfect square , the nature of the roots are irrational and not equal.
» hence , the correct answer is B ( the roots are irrational and are not equal.
4. Since k>0 , the nature of the roots are real irrational and are not equal.
» hence , it has 2 real roots and the correct answer is B(two real roots)
5. Given: x²-10x=-9 » x²-10x+9=0
Solving the roots using factoring,
» hence , the roots are 9 and 1 and the correct answer is B (1 and 9)