(x-1)²=2x+3 form the equation as ax²+bx+c=0
Answers
Answer:
= [-b±√(b^2 -4ac)]/2a
so assume that x=[-b+√(b^2–4ac)]/2a is the common root.
So, for the roots of the given equation (eq.1, x^2+2x+3=0) will be
x= [-2±√(2^2–4(1)(3))]/2(1)
But we have selected [-b+√(b^2–4ac)]/2a as the common root.
so as per the question,
x= [-b+√(b^2–4ac)]/2a = [-2+√(2^2–4(1)(3))]/2(1)
so now you have the values for a,b, and c
Hence a=1,b=2,c=3
∴a:b:c=1:2:3
If the equation x²+ax+b=0 and x²+bx+a=0 have exactly one common root, then what is the value of a+b?
If x²+3x+5=0 and ax²+bx+c=0 have common roots and a, b and c are natural numbers, then what will be the minimum value of a+b+c?
If ax2+bx+c=0 has equal roots, then what is c equal to?
If the equations ax^2 + bx + a = 0 and x^3 - 2x^2 + 2x - 1 = 0 have two roots in common, is a + b equal to 1, 0, -1, or 2?
Suppose the equation x²+Px+4=0 and x²+Qx+3=0 have a common root, what are these roots in terms of the other two roots?
Suppose, α be the common root of the equations
x²+2x+3=0
and ax²+bx+c=0
Therefore α²+2α+3=0
Or, α²=-(2α+3) ····(1)
And aα²+bα+c=0
Or, aα²=-(bα+c)
Or, α²=-(bα+c)/a·····(2)
from (1) and (2) we get
-(bα+c)/a =-(2α+3)
bα/a+c/a=2α+3
comparing both sides we have
b/a=2
Or b=2a
and c/a=3
Or, c=3a
Now a:b:c=a:2a:3a
Or, a:b:c=1:2:3
Master's in Electric Vehicle Design & Analysis.
The given equation has discriminant less than zero. This means the equation has imaginary roots as the coeffecient of x^2 and x is real.
Therefore the two equations have both roots same. And this is passible when both equations are identical.
a÷1=b÷2=c÷3
Therefore a:b:c=1:2:3
See the solution:
This is something quite obvious if you observe for a while,
x^2+2x+3=0 will have both imaginary roots since its discriminant is less than 0 and it is always the case that imaginary roots occur in conjugate pairs,
Therefore, these equations have both the roots in common or you can say both equations are the same,
This leads to a:b:c=1:2:3
If x2+bx+c=0 has equal roots, then what is b equal to?
If the equation ax2+bx+c=0 has no real roots, then what is b2-4ac?
If the equations x^2+2x+3a=0 and 2x^2+3x+5a=0 have a non-zero common roots, what is a=?
If x² + 2x = 0, what is x?
If ax² + bx + c = 0 and a + b + c = 0, what would be the value(s) of x?
By comparing We get
a=1,b=2,c = 3
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1:2:3
If the equation x²+ax+b=0 and x²+bx+a=0 have exactly one common root, then what is the value of a+b?
If x²+3x+5=0 and ax²+bx+c=0 have common roots and a, b and c are natural numbers, then what will be the minimum value of a+b+c?
If ax2+bx+c=0 has equal roots, then what is c equal to?
If the equations ax^2 + bx + a = 0 and x^3 - 2x^2 + 2x - 1 = 0 have two roots in common, is a + b equal to 1, 0, -1, or 2?
Suppose the equation x²+Px+4=0 and x²+Qx+3=0 have a common root, what are these roots in terms of the other two roots?
If x2+bx+c=0 has equal roots, then what is b equal to?
If the equation ax2+bx+c=0 has no real roots, then what is b2-4ac?
If the equations x^2+2x+3a=0 and 2x^2+3x+5a=0 have a non-zero common roots, what is a=?
If x² + 2x = 0, what is x?
If ax² + bx + c = 0 and a + b + c = 0, what would be the value(s) of x?
If ax²+bx+c=0 has equal roots, then what is b equal to?
If f(x) =ax^2+bx+c has no zeroes and a+b+c is less than zero then A) c=0 B) c>0 C) c<0?
If the roots of ax2+bx+c=0 are equal then the equal root is what?
If one root of the equations, x²+ bx + a = 0 and x² + ax + b = 0 is common and a≠b, what is the relationship between 'a' and 'b'?
If the quadratic equation x2+bx+ac=0 and x2+cx+ab=0 have a common root prove that the equation containing their other roots is x2+ax+bc=0 ?
Answer:
X^2+1-2X = 2X +3
X^2+1-3=4X
X^2-2-4X=0
X^2+(-4)X+(-2)=0