Question

find the nature of roots by calculating the value of discrimination in each case. ☝️​

Answer 1

Step-by-step explanation:

x

2

+10x−7=0

view step

ax^{2}+bx+c=0

\frac{-b±\sqrt{b^{2}-4ac}}{2a}

±

x=\frac{-10±\sqrt{10^{2}-4\left(-7\right)}}{2}

x=

2

−10±

10

2

−4(−7)

view step

10

x=\frac{-10±\sqrt{100-4\left(-7\right)}}{2}

x=

2

−10±

100−4(−7)

view step

-4-7

x=\frac{-10±\sqrt{100+28}}{2}

x=

2

−10±

100+28

view step

10028

x=\frac{-10±\sqrt{128}}{2}

x=

2

−10±

128

view step

128

x=\frac{-10±8\sqrt{2}}{2}

x=

2

−10±8

2

view step

x=\frac{-10±8\sqrt{2}}{2}

±-108\sqrt{2}\approx 11.313708499

x=\frac{8\sqrt{2}-10}{2}

x=

2

8

2

−10

view step

-10+8\sqrt{2}\approx 1.313708499

2

x=4\sqrt{2}-5

x=4

2

−5

view step

x=\frac{-10±8\sqrt{2}}{2}

±8\sqrt{2}\approx 11.313708499

-10

x=\frac{-8\sqrt{2}-10}{2}

x=

2

−8

2

−10

view step

-10-8\sqrt{2}\approx -21.313708499

2

x=-4\sqrt{2}-5

x=−4

2

−5

view step

ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)

-5+4\sqrt{2}\approx 0.656854249

x_{1}

-5-4\sqrt{2}\approx -10.656854249

x_{2}

x^{2}+10x-7=\left(x-\left(4\sqrt{2}-5\right)\right)\left(x-\left(-4\sqrt{2}-5\right)\right)

x

2

+10x−7=(x−(4

2

−5))(x−(−4

2

−5))