Answer:
Discriminant:
[tex]\large \tt {1.\:\: x^2+4x-7=0}[/tex]
[tex]\large \tt {b^{2} -4ac = 4^{2} - 4(1)(-7)}[/tex]
[tex]\large \tt {= 16 - (-28)}[/tex]
[tex]\large \tt{= 44}[/tex]
[tex]\large \tt {2.\:\: 2x^2-x+30=0}[/tex]
[tex]\large \tt {b^{2} -4ac = (-1)^{2} - 4(2)(30)}[/tex]
[tex]\large \tt {= 1 - 240}[/tex]
[tex]\large \tt {= -239}[/tex]
[tex]\large \tt {3.\:\: x^2-14x+49=0}[/tex]
[tex]\large \tt {b^{2} -4ac = 14^{2} - 4(1)(49)}[/tex]
[tex]\large \tt {= 196 - 196}[/tex]
[tex]\large \tt {= 0}[/tex]
[tex]\large \tt {4.\:\: x^2-x+\frac{1}{4} =0}[/tex]
[tex]\large \tt {b^{2} -4ac = (-1)^{2} - 4(1)(0.25)}[/tex]
[tex]\large \tt {= 1 - 1}[/tex]
[tex]\large \tt {= 0}[/tex]
[tex]\large \tt {5.\:\: 8x^2+11x+1 =0}[/tex]
[tex]\large \tt {b^{2} -4ac = 11^{2} - 4(8)(1)}[/tex]
[tex]\large \tt {= 121 - 32}[/tex]
[tex]\large \tt {= 89}[/tex]
[tex]\large \tt {6.\:\: 6x^2+5x+2 =0}[/tex]
[tex]\large \tt {b^{2} -4ac = 5^{2} - 4(6)(2)}[/tex]
[tex]\large \tt {= 25- 48}[/tex]
[tex]\large \tt {= -23}[/tex]
[tex]\large \tt {7.\:\: 9x^2-x-10 =0}[/tex]
[tex]\large \tt {b^{2} -4ac = (-1)^{2} - 4(9)(10)}[/tex]
[tex]\large \tt {= 1- 360}[/tex]
[tex]\large \tt {= -359}[/tex]
[tex]\large \tt {8.\:\: 5x^2+12x-\frac{1}{2} =0}[/tex]
[tex]\large \tt {b^{2} -4ac = 0^{2} - 4(5)(11.5)}[/tex]
[tex]\large \tt {= 0-230}[/tex]
[tex]\large \tt {= -230}[/tex]
[tex]\large \tt {9.\:\: 3x^2-\frac{1}{2} x+\frac{1}{4} =0}[/tex]
[tex]\large \tt {b^{2} -4ac = (-0.5)^{2} - 4(3)(0.25)}[/tex]
[tex]\large \tt {= 0.25-3}[/tex]
[tex]\large \tt {= -2.75}[/tex]
Nature Of Roots
[tex]\large \tt{1.\:Two\:unequal\:real\:roots}[/tex]
[tex]\large \tt{2.\:No\:real\:roots}[/tex]
[tex]\large \tt{3.\:Two\:equal\:real\:roots}[/tex]
[tex]\large \tt{4.\:Two\:equal\:real\:roots}[/tex]
[tex]\large \tt{5.\:Two\:unequal\:real\:roots}[/tex]
[tex]\large \tt{6.\:No\:real\:roots}[/tex]
[tex]\large \tt{7.\:No\:real\:roots}[/tex]
[tex]\large \tt{8.\:No\:real\:roots}[/tex]
[tex]\large \tt{9.\:No\:real\:roots}[/tex]
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Answers & Comments
Verified answer
Answer:
Discriminant:
[tex]\large \tt {1.\:\: x^2+4x-7=0}[/tex]
[tex]\large \tt {b^{2} -4ac = 4^{2} - 4(1)(-7)}[/tex]
[tex]\large \tt {= 16 - (-28)}[/tex]
[tex]\large \tt{= 44}[/tex]
[tex]\large \tt {2.\:\: 2x^2-x+30=0}[/tex]
[tex]\large \tt {b^{2} -4ac = (-1)^{2} - 4(2)(30)}[/tex]
[tex]\large \tt {= 1 - 240}[/tex]
[tex]\large \tt {= -239}[/tex]
[tex]\large \tt {3.\:\: x^2-14x+49=0}[/tex]
[tex]\large \tt {b^{2} -4ac = 14^{2} - 4(1)(49)}[/tex]
[tex]\large \tt {= 196 - 196}[/tex]
[tex]\large \tt {= 0}[/tex]
[tex]\large \tt {4.\:\: x^2-x+\frac{1}{4} =0}[/tex]
[tex]\large \tt {b^{2} -4ac = (-1)^{2} - 4(1)(0.25)}[/tex]
[tex]\large \tt {= 1 - 1}[/tex]
[tex]\large \tt {= 0}[/tex]
[tex]\large \tt {5.\:\: 8x^2+11x+1 =0}[/tex]
[tex]\large \tt {b^{2} -4ac = 11^{2} - 4(8)(1)}[/tex]
[tex]\large \tt {= 121 - 32}[/tex]
[tex]\large \tt {= 89}[/tex]
[tex]\large \tt {6.\:\: 6x^2+5x+2 =0}[/tex]
[tex]\large \tt {b^{2} -4ac = 5^{2} - 4(6)(2)}[/tex]
[tex]\large \tt {= 25- 48}[/tex]
[tex]\large \tt {= -23}[/tex]
[tex]\large \tt {7.\:\: 9x^2-x-10 =0}[/tex]
[tex]\large \tt {b^{2} -4ac = (-1)^{2} - 4(9)(10)}[/tex]
[tex]\large \tt {= 1- 360}[/tex]
[tex]\large \tt {= -359}[/tex]
[tex]\large \tt {8.\:\: 5x^2+12x-\frac{1}{2} =0}[/tex]
[tex]\large \tt {b^{2} -4ac = 0^{2} - 4(5)(11.5)}[/tex]
[tex]\large \tt {= 0-230}[/tex]
[tex]\large \tt {= -230}[/tex]
[tex]\large \tt {9.\:\: 3x^2-\frac{1}{2} x+\frac{1}{4} =0}[/tex]
[tex]\large \tt {b^{2} -4ac = (-0.5)^{2} - 4(3)(0.25)}[/tex]
[tex]\large \tt {= 0.25-3}[/tex]
[tex]\large \tt {= -2.75}[/tex]
Nature Of Roots
[tex]\large \tt{1.\:Two\:unequal\:real\:roots}[/tex]
[tex]\large \tt{2.\:No\:real\:roots}[/tex]
[tex]\large \tt{3.\:Two\:equal\:real\:roots}[/tex]
[tex]\large \tt{4.\:Two\:equal\:real\:roots}[/tex]
[tex]\large \tt{5.\:Two\:unequal\:real\:roots}[/tex]
[tex]\large \tt{6.\:No\:real\:roots}[/tex]
[tex]\large \tt{7.\:No\:real\:roots}[/tex]
[tex]\large \tt{8.\:No\:real\:roots}[/tex]
[tex]\large \tt{9.\:No\:real\:roots}[/tex]