Determine the nature of roots of the following quadratic equations using the discriminant.
1. x^2 + 5x = 4
discriminant:
Nature of roots:
2. -4x^2 = 8x -3
discriminant:
Nature of roots:
3. 10x- 1= 4x^2
Discriminant:
Nature of roots:
4. 15 + 8x - 3x^2 =0
Discriminant:
Nature of roots:
5. 9x^2 - 6x = -9
Discriminant:
Nature of roots:
1. x^2 + 5x = 4
discriminant:
Nature of roots:
2. -4x^2 = 8x -3
discriminant:
Nature of roots:
3. 10x- 1= 4x^2
Discriminant:
Nature of roots:
4. 15 + 8x - 3x^2 =0
Discriminant:
Nature of roots:
5. 9x^2 - 6x = -9
Discriminant:
Nature of roots:
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Answer:
In finding the Nature of Roots, Find the Discriminant using the formula b²-4ac
1. x²+5x-4
5²-4(1)(-4)
25+16= 41
Nature of Roots is Real Irrational Unequal
2. -4x²-8x+3
-8²-4(-4)(3)
64+48= 112
Nature of Roots is Real Irrational Unequal
3. -4x²+10x-1
10²-4(-4)(-1)
100-16= 84
Nature of Roots is Real Irrational Unequal
4. -3x²+8x+15
8²-4(-3)(15)
64+180= 244
Nature of Roots is Real Irrational Unequal
5. 9x²-6x+9
-6²-4(9)(9)
36-324= -288
Nature of Roots is Not Real
Nature of Roots