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Bas_tet [7]
3 years ago
9

Which value of b will cause the quadratic equation x^2+bx+5=0 to have two real number solution

Mathematics
2 answers:
Westkost [7]3 years ago
7 0

Answer:

Every value of b>4.47 and b<-4.47 will cause the quadratic equation x^2+bx+5=0 to have two real number solution.

Step-by-step explanation:

We have the quadratic function x^2+bx+5=0, and we have to find the value of b.

A <em>quadratic function</em> is ax^2+bx+c=0, a\neq 0, a quadratic function usually has two real solutions. You can find that solutions using Bhaskara's Formula:

x_1=\frac{-b+\sqrt{b^2-4.a.c} }{2.a}

x_2=\frac{-b-\sqrt{b^2-4.a.c} }{2.a}

x_1 and x_2 are real solutions of the quadratic equation if and only if:

b^2-4.a.c >0

If b^2-4.a.c the quadratic equation doesn't have real solutions.

If  b^2-4.a.c =0  the quadratic equation has only one solution.

Then in this case to have two real number solutions: b^2-4.a.c >0

We have x^2+bx+5=0, where a=1, b, c=5

Then,

b^2-4.a.c >0\\b^2-4.1.5>0\\b^2-20>0

Adding 20 in both sides of the equation:

b^2-20>0\\b^2-20+20>20\\b^2>20\\b>\sqrt{20}

Which is the same as: b

Then, b>\sqrt{20}\\b>4.47\\b

Then every value of b>4.47 and b<-4.47 will cause the quadratic equation x^2+bx+5=0 to have two real number solution.

For example b=-5 or b=5.

If you replace with b=-5 in b^2-4.a.c >0

b^2-4.a.c >0\\(-5)^2-4.1.5>0\\25-20>0\\5>0

Then the quadratic function has two real number solutions.

Aloiza [94]3 years ago
5 0
To have 2 real number solutions  the discriminant b^2 - 4ac  must be greater than zero.

so the condition  for 2 real roots in this equation is:-

b^2 - 4*1*5 > 0
b^2 >  20

b > sqrt 20    ( positive root)    Answer
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