Advertisements
Advertisements
प्रश्न
`x+1/x=3,x≠0`
उत्तर
The given equation is
`x+1/x=3,x≠0`
⇒` (x^2+1)/x=3 `
⇒ `x^2+1=3x`
⇒`x^2-3x+1=0`
This equation is of the form `ax^2+bx+c=0,` where, `a=1, b=-3 and c=1`
∴ Discriminant,` D=b^2-4ac=(-3)^2-4xx1xx1=9-4=5>0`
So, the given equation has real roots.
Now, `sqrtD=sqrt5`
∴`a=(-b+sqrtD)/(2a)=(-(-3)+sqrt5)/(2xx1)=(3+sqrt5)/2`
β=(-b-sqrtD)/(2a)=(-(-3)-sqrt5)/(2xx1)=(3-sqrt5)/2`
Hence, `(3+sqrt5)/2` and `(3-sqrt5)/2` are the roots of the given equation.
APPEARS IN
संबंधित प्रश्न
Write the discriminant of the following quadratic equations:
x2 - x + 1 = 0
`25x^2+30x+7=0`
`x^2+x+2=0`
`36x^2-12ax+(a^2-b^2)=0`
`x^2+6x-(a^2+2a-8)=0`
`12abx^2-(9a^2-8b^2)x-6ab=0,` `Where a≠0 and b≠0`
The denominator of a fraction is 3 more than its numerator. The sum of the fraction and its reciprocal is `2 9/10` Find the fraction.
For what value of k, are the roots of the quadratic equation kx (x − 2) + 6 = 0 equal ?
For what values of k, the roots of the quadratic equation (k + 4) x2 + (k + 1) x + 1 = 0 are equal ?
Find the discriminant of the quadratic equation 4x2 – 5 = 0 and hence comment on the nature of roots of the equation.
