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Posted by Dajshay Prithiv 6 years ago
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Yogita Ingle 6 years ago
Given, equation is x2 + kx + 2 = 0
Given, roots are equal, so its discriminant value will be equal to zero
=> D = 0
=> b2 - 4ac = 0 .............1
On comapring the given equation with ax2 + bx + c = 0, we get
a = 1, b = k, c = 2
From equation 1, we get
=> (k)2 - 4 * 1 * 2 = 0
=> k2 - 8 = 0
=> k2 = 8
=> k = ±√8
=> k = ±2√2
So, the value of k is k = ±2√2
Posted by Rajnish Yadav 6 years ago
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Gaurav Seth 6 years ago
In an AP,
First term (a) = 5
Last term (l) = 45
Sum of the terms of the AP (Sn) = 400
Number of terms = (n) = ?
Common difference = (d) = ?
Now,
Sn = n/2 × (a + l)
=> 400 = n/2 × (5 + 45)
=> n/2 × 50 = 400
=> n = (400 × 2)/50
=> n = 16
Posted by Zeeshan Khan 6 years ago
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☮?Amiable Buddy?☮ 6 years ago
Yogita Ingle 6 years ago
Therefore, S = 1 + 2 + 3 + 4 + 5 + .................... + 100
Clearly, it is an Arithmetic Progression whose first term = 1, last term = 100 and number of terms = 100.
Therefore, S = {tex}\frac{100}{2} {/tex}(100 + 1)
= 50(101)
= 5050
Therefore, the sum of first 100 natural numbers is 5050.
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Yogita Ingle 6 years ago
Let the sides of first and second square be X and Y .
Area of first square = (X)²
And,
Area of second square = (Y)²
According to question,
(X)² + (Y)² = 544 m² ------------(1).
Perimeter of first square = 4 × X
and,
Perimeter of second square = 4 × Y
According to question,
4X - 4Y = 32 -----------(2)
From equation (2) we get,
4X - 4Y = 32
4(X-Y) = 32
X - Y = 32/4
X - Y = 8
X = 8+Y ---------(3)
Putting the value of X in equation (1)
(X)² + (Y)² = 544
(8+Y)² + (Y)² = 544
(8)² + (Y)² + 2 × 8 × Y + (Y)² = 544
64 + Y² + 16Y + Y² = 544
2Y² + 16Y - 544 +64 = 0
2Y² + 16Y -480 = 0
2( Y² + 8Y - 240) = 0
Y² + 8Y - 240 = 0
Y² + 20Y - 12Y -240 = 0
(Y+20) (Y-12) = 0
(Y+20) = 0 Or (Y-12) = 0
Y = -20 OR Y = 12
Putting Y = 12 in EQUATION (3)
X = 8+Y = 8+12 = 20
Side of first square = X = 20 m
and,
Side of second square = Y = 12 m.
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