Choose the letter of the correct answer in the given set of choices. Write the letter of your choice on the space before the number. Write E if NONE of the choices is the correct answer. Use CAPITAL LETTER.
_____1. Transform 1/x + x/6 = 2/3 into quadratic equation
x2 + 4x – 6 = 0 B. x2 + 6x - 4 = 0 C. x2 – 11x - 24= 0 D. x2 + 11x - 24= 0
_____2. In item #1, what is the Least Common Multiple ( LCM) of the denominators.
6 B. x C. 6x D. 18x
_____3. A rectangle has a perimeter of 38 cm and an area of 90 cm2. Find the dimension of the rectangle.
9 & 10 B. 2 & 45 C. 30 & 8 D. 3 & 30
_____4. Find the roots of quadratic equation x2 + 5x – 6= 0
-6 &1 B. -2 & - 3 C. -1 & 6 D. 2 & 3
_____5. Find two consecutive even integers whose product is 624?
22 & 24 B. 23 & 24 C. 24 & 26 D. 26 & 28
____6. Find two consecutive odd integers whose product is 99.
9 & 11 B. 9 & -11 C. 8 &11 D. – 9 & 11
_____7.If the square of a number is added to thrice the number, the sum is 108. Find the number.
A. 9 B. 8 C. -9 D. 12
____8. Find three consecutive positive odd integers such that the product of the first and the third is 32 more than 5 times the second.
A. 5, 7, 9 B. 7, 9, 11 C. 9, 11, 13 D. 11, 13, 15
____ 9. The length of a garden is 5m longer than its width and the area is 14m2. How long is the garden?
9 m B. 7 m C. 5 m D. 2 m
____10. It takes Carl 3 hours more to do a job than it takes Jane. If they work together, they finish the same
job in 2 hours. How long would it take Carl to finish the job alone?
3 hours B. 5 hours C. 6 hours D. 8 hours
____11. Find the roots of x+ 8/(x-2)=1+ 4x/(x-2) .
5 & 2 B. – 5 & 2 C. – 5 & - 2 D. 7 & -5
____12. In item # 11 what is the resulting quadratic equation in standard form?
x2 + 7x + 10 = 0 C. x2 – 7x – 10 = 0
x2 – 7x + 10 = 0 D. x2 + 7x – 10 = 0
____ 13. What is the Least Common Multiple ( LCM) of denominators in equation 6/x+ (x-3)/4=2.
4x B. 8x C. 6x D. x
____ 14. In equation 6/x+ (x-3)/4=2 what is the resulting quadratic equation in standard form?
x2 + 11x -24 = 0 C. x2 + 7x – 10 = 0
x2 -11x + 24 = 0 D. x2 – 11x + 24 = 0
____15. Find the solution of the equation 6/x+ (x-3)/4=2.
-3 & - 8 B. 3 & 8 C. -8 & 3 D. 8 & -3
II. Transform each of the following equations to quadratic equation in the form of ax2 + bx + c = 0
__________________ 16. (s + 6 ) 2 = 15
__________________ 17. a (a – 2) = 5
__________________ 18. (2x^2)/5+ 5x/4=10
__________________ 19. 2/(t )+ 3t/2=2
__________________ 20. 3x ( x – 2 ) = 12x
Answers
Answer:
Find the roots of x+ 8/(x-2)=1+ 4x/(x-2) .
5 & 2 B. – 5 & 2 C. – 5 & - 2 D. 7 & -5
____12. In item # 11 what is the resulting quadratic equation in standard form?
x2 + 7x + 10 = 0 C. x2 – 7x – 10 = 0
x2 – 7x + 10 = 0 D. x2 + 7x – 10 = 0
Step-by-step explanation:
hope it helps yOu.
Answer:
The roots of quadratic equation are the values of the variable that satisfy the equation. They are also known as the "solutions" or "zeros" of the quadratic equation. For example, the roots of the quadratic equation x2 - 7x + 10 = 0 are x = 2 and x = 5 because they satisfy the equation. i.e.,
when x = 2, 22 - 7(2) + 10 = 4 - 14 + 10 = 0.
when x = 5, 52 - 7(5) + 10 = 25 - 35 + 10 = 0.
But how to find the roots of a general quadratic equation ax2 + bx + c = 0? Let us try to solve it for x by completing the square.
ax2 + bx = - c
Dividing both sides by 'a',
x2 + (b/a) x = - c/a
Here, the coefficient of x is b/a. Half of it is b/(2a). Its square is b2/4a2. Adding b2/4a2 on both sides,
x2 + (b/a) x + b2/4a2 = (b2/4a2) - (c/a)
[ x + (b/2a) ]2 = (b2 - 4ac) / 4a2 (using (a + b)² formula)
Taking square root on both sides,
x + (b/2a) = ±√ (b² - 4ac) / 4a²
x + (b/2a) = ±√ (b² - 4ac) / 2a
Subtracting b/2a from both sides,
x = (-b/2a) ±√ (b² - 4ac) / 2a (or)
x = (-b ± √ (b² - 4ac) )/2a
This is known as the quadratic formula and it can be used to find any type of roots of a quadratic equation.