5. How many real roots does the quadratic equation x2 + 5x + 7 = 0 have?
A. O
C. 2
B. 1
D. infinite
6. In solving the equation x2 + 14x = 32 by completing the square, what will be added to both sides of the
equation to make the left side of the equation a perfect square trinomial?
A.7
C. 49
B. 14
D. 2401
7. Your classmate said that the roots of 3x2 - 7x - 6 = 0 are (-3, 3). Is he correct? If not, why not?
A. No, the roots are (3, 3). C. No, the roots are (3, -3).
B. Yes, the roots are (-3,13). D. No, the roots are (-3, -3)
.
8. The sum of two numbers is 16, and the sum of their squares is 146. Find the two numbers.
A. 14 and 2
C. -11 and 5
B. 11 and 5
D. -14 and -2
plss paki sagot
Answers
Answer:
option D is the answer mmmmm
Given: x² + 5x + 7 = 0
To Find : How many real roots does the quadratic equation have
Solution:
x² + 5x + 7 = 0
Quadratic equation is of the form ax²+bx+c=0 where a , b and c are real also a≠0.
b²-4ac is called discriminant.
b²-4ac >0 roots are real and distinct
b²-4ac =0 roots are real and equal
b²-4ac < 0 roots are imaginary ( not real )
x² + 5x + 7 = 0
a = 1 , b = 5 , c = 7
b² - 4ac = 5² - 4(1)(7) = - 3 < 0
Hence roots are imaginary ( not real )
So there are 0 real roots
x² + 14x = 32
Add 49 both sides to make complete square
=> x² + 14x + 49 = 32 + 49
=> (x + 7)² = 9²
3x² - 7x - 6 = 0
3x² - 9x + 2x - 6 = 0
=> 3x(x - 3) + 2(x - 3) = 0
=> (x - 3)(3x + 2) = 0
=> x = 3 , x = - 2/3
Root are 3 ,- 2/3
The sum of two numbers is 16, and the sum of their squares is 146
11 and 5
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