Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
48x2 − 13x − 1 = 0
Advertisements
उत्तर
We have been given
48x2 - 13x - 1 = 0
48x2 - 16x + 3x - 1 = 0
16x(3x - 1) + 1(3x - 1) = 0
(16x + 1)(3x - 1) = 0
Therefore,
16x + 1 = 0
16x = -1
x = -1/16
or,
3x - 1 = 0
3x = 1
x = 1/3
Hence, x = -1/16 or x = 1/3
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equation for x:
`x^2+(a/(a+b)+(a+b)/a)x+1=0`
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
If an integer is added to its square, the sum is 90. Find the integer with the help of quadratic equation.
Find the two consecutive natural numbers whose product is 20.
The hypotenuse of a right triangle is `3sqrt10`. If the smaller leg is tripled and the longer leg doubled, new hypotenuse wll be `9sqrt5`. How long are the legs of the triangle?
Some students planned a picnic. The budget for food was Rs. 500. But, 5 of them failed to go and thus the cost of food for each member increased by Rs. 5. How many students attended the picnic?
Solve the following quadratic equations by factorization:
`100/x-100/(x+5)=1`
If the quadratic equation (c2 – ab) x2 – 2 (a2 – bc) x + b2 – ac = 0 in x, has equal roots, then show that either a = 0 or a3 + b3 + c3 = 3abc ?
Solve for x: `3x^2-2sqrt3x+2=0`
Determine whether the values given against the quadratic equation are the roots of the equation.
x2 + 4x – 5 = 0 , x = 1, –1
In the following determine the set of values of k for which the given quadratic equation has real roots: \[2 x^2 + x + k = 0\]
Find the value of p for which the quadratic equation
\[\left( p + 1 \right) x^2 - 6(p + 1)x + 3(p + 9) = 0, p \neq - 1\] has equal roots. Hence, find the roots of the equation.
Disclaimer: There is a misprinting in the given question. In the question 'q' is printed instead of 9.
Solve the following equation: 4x2 - 13x - 12 = 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.
The sum of the square of two numbers is 233. If one of the numbers is 3 less than twice the other number. Find the numbers.
Car A travels x km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
Write down the number of litres of petrol used by car A and car B in covering a distance of 400 km.
In each of the following determine whether the given values are solutions of the equation or not.
x2 + x + 1 = 0; x = 1, x = -1.
Solve the following equation by factorization
3x2 – 5x – 12 = 0
Solve the following equation by factorisation :
2x2 + ax – a2= 0
Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.
