+1234 One root of the quadratic equation $x^2 + bx -28 = 4x + 14$ is $-7$. What is the value of $b$?
+1281
One root of the quadratic equation $x^2 + bx -28 = 4x + 14$ is $-7$. What is the value of $b$?
x2 + bx – 28 = 4x + 14
Change that "bx" to "kx" because I have another use for "b".
Arrange terms in standard quadratic format ax2 + bx + c = 0
x2 + kx – 4x – 42 = 0
x2 + (kx – 4x) – 42 = 0
x2 + (k – 4) x – 42 = 0 and it's given that one root is – 7
Since one root is – 7, the other root has to be + 6 to get that – 42
so, factored, we have (x + 7)(x – 6) which multiplied out is x2 + x – 42
& so, (k – 4) x = x which means that k = + 5 or, reverting to the words of the problem, b = 5
.
+1281
One root of the quadratic equation $x^2 + bx -28 = 4x + 14$ is $-7$. What is the value of $b$?
x2 + bx – 28 = 4x + 14
Change that "bx" to "kx" because I have another use for "b".
Arrange terms in standard quadratic format ax2 + bx + c = 0
x2 + kx – 4x – 42 = 0
x2 + (kx – 4x) – 42 = 0
x2 + (k – 4) x – 42 = 0 and it's given that one root is – 7
Since one root is – 7, the other root has to be + 6 to get that – 42
so, factored, we have (x + 7)(x – 6) which multiplied out is x2 + x – 42
& so, (k – 4) x = x which means that k = + 5 or, reverting to the words of the problem, b = 5
.
