Advertisements
Advertisements
प्रश्न
`7x^2+3x-4=0`
Advertisements
उत्तर
`7x^2+3x-4=0`
⇒`49x^2+21x-28=0` (Multiplying both sides by 7)
⇒`49x^2+21x=28`
⇒`(7x)^2+xx7x xx3/2+(3/2)^2=28+(3/2)^2` [Adding (3/2)^2 on both sides]
⇒`(7x+3/2)^2=28+9/4=121/4=(11/2)^2`
⇒`7x+3/2=+-11/2` (Taking square root on both sides)
⇒`7x+3/2=11/2 or 7x+3/2=-11/2`
⇒`7x=11/2-3/2=8/2=4 or 7x=11/2-3/2=-14/2=-7`
⇒`x=4/7 or x=-1`
Hence, `4/7 and -1` are the roots of the given equation.
APPEARS IN
संबंधित प्रश्न
Solve for x: `(x-3)/(x-4)+(x-5)/(x-6)=10/3; x!=4,6`
Solve for x :
`1/(x + 1) + 3/(5x + 1) = 5/(x + 4), x != -1, -1/5, -4`
Solve the following quadratic equations by factorization:
`x^2-(sqrt2+1)x+sqrt2=0`
Rs. 9000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs. 160 less. Find the original number of persons.
Solve each of the following equations by factorization:
`9/2x=5+x^2`
Determine whether the values given against the quadratic equation are the roots of the equation.
x2 + 4x – 5 = 0 , x = 1, –1
Solve the following quadratic equation by factorisation.
25m2 = 9
Find the values of k for which the roots are real and equal in each of the following equation:\[px(x - 3) + 9 = 0\]
Find the values of k for which the quadratic equation
\[\left( 3k + 1 \right) x^2 + 2\left( k + 1 \right)x + 1 = 0\] has equal roots. Also, find the roots.
Write the set of value of 'a' for which the equation x2 + ax − 1 = 0 has real roots.
Write the set of value of k for which the quadratic equations has 2x2 + kx − 8 = 0 has real roots.
If \[x^2 + k\left( 4x + k - 1 \right) + 2 = 0\] has equal roots, then k =
Solve equation using factorisation method:
2(x2 – 6) = 3(x – 4)
Solve equation using factorisation method:
(x + 1)(2x + 8) = (x + 7)(x + 3)
Solve equation using factorisation method:
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2 1/2`
Solve the following equation by factorization
2x2 – 8x – 24 = 0 when x∈I
A two digit number contains the bigger at ten’s place. The product of the digits is 27 and the difference between two digits is 6. Find the number.
The length of a rectangular garden is 12 m more than its breadth. The numerical value of its area is equal to 4 times the numerical value of its perimeter. Find the dimensions of the garden.
If the sum of the roots of the quadratic equation ky2 – 11y + (k – 23) = 0 is `13/21` more than the product of the roots, then find the value of k.
Find the roots of the quadratic equation x2 – x – 2 = 0.
