If a 0 and b

Question

If a > 0 and b < 0, which of the following statements are true about the values of x that solve the equation  x^2 − ax + b = 0  ?

I. They have opposite signs.
II. Their sum is greater than Zero.
III. Their product equals -b

A. I only
B. II only
C. I and II only
D. I and III only
E. I, II and III

chetan2u · Accepted Answer

If the quadratic equation is  ax^2+bx+c=0 ,
Sum of roots =  \frac{-b}{a} 
Product of roots =  \frac{c}{a}

I. They have opposite signs.
II. Their sum is greater than Zero.
III. Their product equals -b

x^2 -ax + b = 0  is the quadratic equation here.
Sum of roots =  \frac{(-a)}{1}=a 
Product of roots =  \frac{b}{1}=b

I. They have opposite signs.
Product of the two roots is b. =>  x_1*x_2=b<0 .
Thus the product of two roots is NEGATIVE, and it is possible only when they have opposite sign.
True

II. Their sum is greater than Zero.
  x_1+x_2=a>0 .
True

III. Their product equals -b
  x_1*x_2=b .
False

I and II

C

SherzodAzamov · Answer

let's rewrite the equation
x^2 − (+a)*x + (-b) = 0
for simplicity let's change a and b to numbers
a = 6
b = -5
x^2 − 6*x − 5 = 0

the equation has two roots, x1 and x2
x1 + x2 = 6
x1*x2 = -5

I. They have opposite signs : correct, as their product is negative
II. Their sum is greater than Zero. : correct, as a is greater than 0
III. Their product equals -b : b is negative so -b is not negative

so the answer is C 
Help me if I am wrong)

anjanita · Answer

The answer is C

x^2−ax+b=0

If we were to FACTOR x^2 - ax + b into the form (x + k)(x + j), we'd have two clues to help us.

First, we know that the product jk must equal b.
Since we're told that b is NEGATIVE, we know that one of the variables (j or k) is POSITIVE, and the other is NEGATIVE....So, statement 1 is true

The two values of x are = (a + (√(a^2 - 4*b)))/2 & (a - (√(a^2 - 4*b)))/2

The sum of these two values is = a which is >0...So, statement 2 is true

The product of two values is (a^2 - a^2 +4*b)/4 = b, so the statement 3 is not true

Therefore, the answer is C

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If a > 0 and b < 0, which of the following statements are true about

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