1)Solve by factoring:5x^2=4-19x
answer=-4,1/5
2)Which quadratic equation has roots 7 and -2/3?
answer=A
A.2x^2-11x-21=0
B.3x^2-19x-14=0
C.3x^2+23x+14=0
D.2x^2+11x-21=0
3)To solve 4x^2-28x+49=25 by using the square root property,you would first rewrite the equation as
answer=(2x-7)^2=25
4)Find the value of c that makes x^2+5x+c a perfect square trinomial.
answer=25/4
5)The quadratic equation x^2-8x=-20 is to be solved by completing the square.Which equation would be a step in that solution?
answer=x^2-8x+16=-20
1)Solve by factoring:5x^2=4-19x
answer=-4,1/5
2)Which quadratic equation has roots 7 and -2/3?
answer=A
A.2x^2-11x-21=0
B.3x^2-19x-14=0
C.3x^2+23x+14=0
D.2x^2+11x-21=0
3)To solve 4x^2-28x+49=25 by using the square root property,you would first rewrite the equation as
answer=(2x-7)^2=25
4)Find the value of c that makes x^2+5x+c a perfect square trinomial.
answer=25/4
5)The quadratic equation x^2-8x=-20 is to be solved by completing the square.Which equation would be a step in that solution?
answer=x^2-8x+16=-20
corection is for number 2 is b
1) To solve the equation 5x^2 = 4 - 19x by factoring, we need to rearrange the terms to one side of the equation to get it in the form ax^2 + bx + c = 0. In this case, we have 5x^2 + 19x - 4 = 0.
Now, we need to factor the quadratic equation. We can use the factored form: (px + q)(rx + s) = 0, where p, q, r, and s are coefficients.
To factor the quadratic equation, we need to find two numbers whose product is equal to the product of the coefficient of x^2 (which is 5) and the constant term (which is -4), and whose sum is equal to the coefficient of x (which is 19). In this case, the numbers are 20 and -1.
So, we can write the equation as (5x - 1)(x + 4) = 0.
Setting each factor equal to zero, we get 5x - 1 = 0 or x + 4 = 0.
Solving these equations, we find x = 1/5 or x = -4.
Therefore, the solutions to the equation 5x^2 = 4 - 19x are x = -4 and x = 1/5.
2) To determine which quadratic equation has roots 7 and -2/3, we can use the fact that the roots of a quadratic equation in the form ax^2 + bx + c = 0 are given by the formula x = (-b ± √(b^2 - 4ac))/(2a).
In this case, we have two roots: x = 7 and x = -2/3.
Let's substitute these values into the formula and see which equation satisfies them.
For option A, we have 2x^2 - 11x - 21 = 0.
Substituting x = 7, we get 2(7)^2 - 11(7) - 21 = 0, which is not equal to zero.
Substituting x = -2/3, we get 2(-2/3)^2 - 11(-2/3) - 21 = 0, which is not equal to zero.
Therefore, option A is not the correct quadratic equation with roots 7 and -2/3.
Similarly, we should check the other options.
For option B: 3x^2 - 19x - 14 = 0.
Substituting x = 7, we get 3(7)^2 - 19(7) - 14 = 0, which is equal to zero.
Substituting x = -2/3, we get 3(-2/3)^2 - 19(-2/3) - 14 = 0, which is also equal to zero.
Therefore, option B, 3x^2 - 19x - 14 = 0, is the quadratic equation with roots 7 and -2/3.
3) To solve the equation 4x^2 - 28x + 49 = 25 by using the square root property, we need to first rewrite the equation in the form (x - p)^2 = q, where p and q are constants.
Subtracting 25 from both sides of the equation, we get 4x^2 - 28x + 49 - 25 = 0.
Simplifying, we have 4x^2 - 28x + 24 = 0.
Next, we need to complete the square. To do this, we take half of the coefficient of x (-28) and square it, which gives us 14^2 = 196.
Adding 196 to both sides of the equation, we get 4x^2 - 28x + 220 = 196.
Now, we can rewrite the left side of the equation as a perfect square trinomial: (2x - 7)^2 = 196.
Taking the square root of both sides, we have 2x - 7 = ± √196.
√196 = ± 14, so we can simplify to 2x - 7 = ± 14.
Now, solving for x, we have two equations:
1) 2x - 7 = 14: Adding 7 to both sides, we get 2x = 21, and dividing by 2, we find x = 10.5.
2) 2x - 7 = -14: Adding 7 to both sides, we get 2x = -7, and dividing by 2, we find x = -3.5.
The solutions to the equation 4x^2 - 28x + 49 = 25 using the square root property are x = 10.5 and x = -3.5.
4) To find the value of c that makes x^2 + 5x + c a perfect square trinomial, we need to complete the square.
For a quadratic trinomial in the form (x + p)^2 = x^2 + 2px + p^2 to be a perfect square trinomial, the constant term should be equal to the square of half the coefficient of x.
In this case, the quadratic trinomial is x^2 + 5x + c. So, we have (x + 5/2)^2 = x^2 + 2(5/2)x + (5/2)^2.
Comparing the quadratic trinomials, we see that the coefficient of x is 5/2, so half of it is 5/4.
Therefore, c = (5/4)^2 = 25/16.
The value of c that makes x^2 + 5x + c a perfect square trinomial is 25/16.
5) To solve the quadratic equation x^2 - 8x = -20 by completing the square, we add the square of half the coefficient of x to both sides of the equation.
The coefficient of x is -8, so half of it is -8/2 = -4. The square of -4 is 16.
Therefore, we add 16 to both sides of the equation: x^2 - 8x + 16 = -20 + 16.
Simplifying, we have (x - 4)^2 = -4.
The equation x^2 - 8x + 16 = -4 would be a step in solving x^2 - 8x = -20 by completing the square.