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If (x – 2) and (x + 3) are the factors of the equation x2 + k1x + k2 = 0, then what are the values of k1 and k2?
- Ak1 = 6, k2 = -1
- Bk1 = 1, k2 = -6
- Ck1 = 1, k2 = 6
- Dk1 = -6, k2 = 1
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CCommunity
Given: (x – 2) and (x + 3) are factors
⇒ Roots of the equation = 2, -3
Putting x = 2 in the given equation, we get
⇒ 22 + 2k1 + k2 = 0
⇒ 2k1 + k2 = - 4 …..(i)
Similarly, Putting x = -3 in the given equation, we get
⇒ (-3) 2 - 3k1 + k2 = 0
⇒ - 3k1 + k2 = -9 ……(ii)
Subtracting (i) and (ii)
⇒ 5k1 = 5
⇒ k1 = 1
Putting value of k1 in (i)
⇒ k2 = -6
∴ k1 = 1 and k2 = -6
⇒ Roots of the equation = 2, -3
Putting x = 2 in the given equation, we get
⇒ 22 + 2k1 + k2 = 0
⇒ 2k1 + k2 = - 4 …..(i)
Similarly, Putting x = -3 in the given equation, we get
⇒ (-3) 2 - 3k1 + k2 = 0
⇒ - 3k1 + k2 = -9 ……(ii)
Subtracting (i) and (ii)
⇒ 5k1 = 5
⇒ k1 = 1
Putting value of k1 in (i)
⇒ k2 = -6
∴ k1 = 1 and k2 = -6