Advertisements
Advertisements
प्रश्न
If the equation x2 − ax + 1 = 0 has two distinct roots, then
पर्याय
|a| = 2
|a| < 2
|a| > 2
None of these
Advertisements
उत्तर
The given quadric equation is x2 − ax + 1 = 0 , and roots are distinct.
Then find the value of a.
Here, a =1,b = a and, c = 1
As we know that `D = b^2 - 4ac`
Putting the value of a =1,b = a and, c = 1
`=(a)^2 - 4 xx 1 xx 1`
` = a^2 - 4`
The given equation will have real and distinct roots, if D > 0
`a^2- 4 > 0`
`a^2 > 4`
` a > 4`
`a > sqrt4`
`> ± 2`
Therefore, the value of |a| > 2.
APPEARS IN
संबंधित प्रश्न
Find the roots of the following quadratic equation by factorisation:
100x2 – 20x + 1 = 0
Solve the following quadratic equations by factorization:
`4sqrt3x^2+5x-2sqrt3=0`
Solve the following quadratic equations by factorization:
`(x-1)/(x-2)+(x-3)/(x-4)=3 1/3`, x ≠ 2, 4
The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.
Solve the following quadratic equations by factorization:
`2(x^2 – 6) = 3 ( x – 4)`
Solve the following quadratic equations by factorization:
`100/x-100/(x+5)=1`
`4x^2+4sqrt3x+3=0`
Solve the following quadratic equations by factorization: \[\sqrt{3} x^2 - 2\sqrt{2}x - 2\sqrt{3} = 0\]
Solve the following quadratic equation by factorization: \[\frac{a}{x - b} + \frac{b}{x - a} = 2\]
Find the value of k for which the following equations have real and equal roots:
\[x^2 + k\left( 2x + k - 1 \right) + 2 = 0\]
Solve the following equation: (x-8)(x+6) = 0
Solve the following equation: `(2"x")/("x" - 4) + (2"x" - 5)/("x" - 3) = 25/3`
Solve the following equation: abx2 +(b2-ac) x - bc = 0
The difference of the square of two natural numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.
Two natural numbers differ by 4. If the sum of their square is 656, find the numbers.
Solve the following quadratic equation by factorisation:
9x2 - 3x - 2 = 0
The perimeter of a rectangular plot is 180 m and its area is 1800 m2. Take the length of the plot as x m. Use the perimeter 180 m to write the value of the breadth in terms of x. Use the values of length, breadth and the area to write an equation in x. Solve the equation to calculate the length and breadth of the plot.
Is 0.2 a root of the equation x2 – 0.4 = 0? Justify
The product of two integers is –18; the integers are ______.
