Advertisements
Advertisements
प्रश्न
If x = 1 is a common roots of the equations ax2 + ax + 3 = 0 and x2 + x + b = 0, then ab =
पर्याय
3
3.5
6
-3
Advertisements
उत्तर
x = 1is the common roots given quadric equation are `ax^2 + ax + 3 = 0`, and `x^2 + x + b= 0`
Then find the value of q.
Here, `ax^2 + ax + 3 = 0 `….. (1)
`x^2 + x + b = 0`….. (2)
Putting the value of x = 1 in equation (1) we get
`a xx 1^2 + a xx 1 +3 = 0`
`a+a + 3 = 0`
`2a = -3`
`a = -3/2`
Now, putting the value of x = 1 in equation (2) we get
`1^2 + 1+b = 0`
`2 +b = 0`
`b = -2`
Then,
`ab = (-3)/2 xx (-2)`
`=3`
APPEARS IN
संबंधित प्रश्न
Find the roots of the following quadratic equation by factorisation:
`sqrt2 x^2 +7x+ 5sqrt2 = 0`
Solve the following quadratic equations by factorization:
`1/x-1/(x-2)=3` , x ≠ 0, 2
The sum of ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man's age at the time. Find their present ages.
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.
`7x^2+3x-4=0`
The sum of natural number and its reciprocal is `65/8` Find the number
Solve the following quadratic equation by factorisation.
x2 – 15x + 54 = 0
Solve the following quadratic equations by factorization: \[\frac{16}{x} - 1 = \frac{15}{x + 1}; x \neq 0, - 1\]
Solve the following quadratic equations by factorization: \[\frac{5 + x}{5 - x} - \frac{5 - x}{5 + x} = 3\frac{3}{4}; x \neq 5, - 5\]
If 1 is a root of the quadratic equation \[3 x^2 + ax - 2 = 0\] and the quadratic equation \[a( x^2 + 6x) - b = 0\] has equal roots, find the value of b.
If \[1 + \sqrt{2}\] is a root of a quadratic equation will rational coefficients, write its other root.
The number of quadratic equations having real roots and which do not change by squaring their roots is
The present age of the mother is square of her daughter's present age. 4 years hence, she will be 4 times as old as her daughter. Find their present ages.
Solve the following quadratic equation by factorisation:
2x2 + ax - a2 = 0 where a ∈ R.
Solve the following quadratic equation:
4x2 - 4ax + (a2 - b2) = 0 where a , b ∈ R.
Solve: x(x + 1) (x + 3) (x + 4) = 180.
The age of a man is twice the square of the age of his son. Eight years hence, the age of the man will be 4 years more than three times the age of his son. Find the present age.
A farmer wishes to grow a 100 m2 rectangular vegetable garden. Since he has with him only 30 m barbed wire, he fences three sides of the rectangular garden letting compound wall of his house act as the fourth side fence. Find the dimensions of his garden.
The product of two successive integral multiples of 5 is 300. Then the numbers are:
The roots of the equation x2 + 3x – 10 = 0 are ______.
