How do use the discriminant to find all values of b for which the equation x^2-bx+4=0x2−bx+4=0 has one real root?

3 Answers
IDKwhatName
Jul 6, 2017

b=+-4b=±4

Explanation:

The discriminant of a quadratic is b^2-4acb2−4ac.

In this case, a=1, b=?, c=-4a=1,b=?,c=−4.

Equal roots means b^2-4ac=0b2−4ac=0

b^2-4(1*4=b^2-16=0b2−4(1⋅4=b2−16=0

b^2=16b2=16

b=+-4b=±4

Ratnaker Mehta
Jul 6, 2017

b=+-4.b=±4.

Explanation:

For the Qudr. Eqn. ax^2+bx+c=0,ax2+bx+c=0, to have only One Root, or, to

have Two Identical Roots,

"The Dicriminant "Delta=b^2-4ac=0.

In our case, (-b)^2-4(1)(4)=b^2-16=0 rArr b=+-4.

Incidentally, if

b=4," the root is, "2; &, if b=-4," the root is "-2.

Tony B
Jul 6, 2017

In y=ax^2+bx+c we have:

b=2sqrt(ac)=+-4

Explanation:

Given the standard form y=ax^2+bx+c

where x=(-b+-sqrt(b^2-4ac))/(2a)

x=-b/(2a)+-sqrt(b^2-4ac)/(2a)

For there to only be 1 real root we need the form

x=(-b)/(2a)+-0

This means that

sqrt(b^2-4ac)/(2a)=0

Multiply both sides by 2a

sqrt(b^2-4ac)=0

square root both sides

b^2-4ac=0

b=sqrt(4ac)=2sqrt(ac)

But a=1 and c=4 giving

b=2sqrt(1xx4)=+-4

Related questions
See all questions in Solutions Using the Discriminant
Impact of this question
5791 views around the world
You can reuse this answer
Creative Commons License