Advertisements
Advertisements
प्रश्न
If x = –2 is the common solution of quadratic equations ax2 + x – 3a = 0 and x2 + bx + b = 0, then find the value of a2b.
उत्तर
Given quadratic equations are
ax2 + x – 3a = 0 ...(i)
x2 + bx + b = 0 ...(ii)
Since, given x = –2 is the common solution of above quadratic equation.
∴ From equations (i),
a(–2)2 + (–2) – 3a = 0
⇒ 4a – 2 – 3a = 0
⇒ a = 2
From equation (ii),
(–2)2 + b(–2) + b = 0
⇒ 4 – 2b + b = 0
⇒ b = 4
Now, a2b = (2)2 × 4 = 4 × 4 = 16
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
`3x^2-2sqrt6x+2=0`
A passenger train takes one hour less for a journey of 150 km if its speed is increased by 5 km/hr from its usual speed. Find the usual speed of the train.
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 length of a hall is 5 m more than its breadth. If the area of the floor of the hall is 84 m2, what are the length and breadth of the hall?
Solve the following quadratic equations by factorization:
`(2x – 3)^2 = 49`
Solve the following equation: `"m"/"n" "x"^2 + "n"/"m" = 1- 2"x"`
The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 124. Determine their present ages.
In each of the following, determine whether the given values are solution of the given equation or not:
2x2 - x + 9 = x2 + 4x + 3; x = 2, x = 3
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.
Is 0.2 a root of the equation x2 – 0.4 = 0? Justify
