B for which -x^2+8x+20=b will have no real roots

Mathematics

1 answer:

Grace [21]3 years ago

3 0

Answer:

Step-by-step explanation:

-x² + 8x + 20 = b

-x² + 8x + 20 - b = 0

a = -1 ; b = 8 ; c = 20 - b

There is no real roots.

So, b² - 4ac < 0

Plug in a, b and c values

8²- 4(-1)(20-b) < 0

When we multiply (-1) and (-4), we will get 4

64 + 4(20 - b) < 0

64 + 4*20 - 4b < 0

64 + 80 - 4b < 0

144 - 4b < 0

Subtract 144 from both sides

-4b < -144

Divide both side by -4 and when we are dividing by (-4), < will change to >

b > -144/-4

b > 36

So, when value of b is greater than 36, the equation will have no real roots.

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Answer:

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$\rule{200}4$

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